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Transient Forward Harmonic Adjoint Sensitivity Analysis (2401.13496v1)

Published 24 Jan 2024 in math.NA and cs.NA

Abstract: This paper presents a transient forward harmonic adjoint sensitivity analysis (TFHA), which is a combination of a transient forward circuit analysis with a harmonic balance based adjoint sensitivity analysis. TFHA provides sensitivities of quantities of interest from time-periodic problems w.r.t. many design parameters, as used in the design process of power-electronics devices. The TFHA shows advantages in applications where the harmonic balance based adjoint sensitivity analysis or finite difference approaches for sensitivity analysis perform poorly. In contrast to existing methods, the TFHA can be used in combination with arbitrary forward solvers, i.e. general transient solvers.

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References (16)
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Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Maas, S.A.: Nonlinear Microwave and RF Circuits. Artech House, Long Beach (2003) (4) Rizzoli, V., Lipparini, A., Marazzi, E.: A general-purpose program for nonlinear microwave circuit design. IEEE Transactions on Microwave Theory and Techniques 31(9), 762–770 (1983). https://doi.org/10.1109/TMTT.1983.1131587 (5) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Rizzoli, V., Lipparini, A., Marazzi, E.: A general-purpose program for nonlinear microwave circuit design. IEEE Transactions on Microwave Theory and Techniques 31(9), 762–770 (1983). https://doi.org/10.1109/TMTT.1983.1131587 (5) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  2. Maas, S.A.: Nonlinear Microwave and RF Circuits. Artech House, Long Beach (2003) (4) Rizzoli, V., Lipparini, A., Marazzi, E.: A general-purpose program for nonlinear microwave circuit design. IEEE Transactions on Microwave Theory and Techniques 31(9), 762–770 (1983). https://doi.org/10.1109/TMTT.1983.1131587 (5) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Rizzoli, V., Lipparini, A., Marazzi, E.: A general-purpose program for nonlinear microwave circuit design. IEEE Transactions on Microwave Theory and Techniques 31(9), 762–770 (1983). https://doi.org/10.1109/TMTT.1983.1131587 (5) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  3. Rizzoli, V., Lipparini, A., Marazzi, E.: A general-purpose program for nonlinear microwave circuit design. IEEE Transactions on Microwave Theory and Techniques 31(9), 762–770 (1983). https://doi.org/10.1109/TMTT.1983.1131587 (5) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  4. Nikolova, N.K., Bandler, J.W., Bakr, M.H.: Adjoint techniques for sensitivity analysis in high-frequency structure CAD. IEEE Transactions on Microwave Theory and Techniques 52(1), 403–419 (2004). https://doi.org/10.1109/TMTT.2003.820905 (6) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  5. Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1), 271–280 (2001). https://doi.org/10.1016/S0378-4754(00)00270-6 (7) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  6. Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964–979 (2008). https://doi.org/10.1016/j.ress.2007.04.002 (8) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  7. Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24, 1076–1089 (2003). https://doi.org/10.1137/S1064827501380630 (9) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  8. Ilievski, Z., Xu, H., Verhoeven, A., Ter Maten, E., Schilders, W., Mattheij, R.: Adjoint transient sensitivity analysis in circuit simulation, 183–189 (2007). https://doi.org/10.1007/978-3-540-71980-9_18 (10) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  9. Bandler, J.W., Zhang, Q.-J., Biernacki, R.: A unified theory for frequency-domain simulation and sensitivity analysis of linear and nonlinear circuits. IEEE Transactions on Microwave Theory and Techniques 36(12), 1661–1669 (1988). https://doi.org/10.1109/22.17397 (11) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  10. Ho, C.-W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems 22(6), 504–509 (1975). https://doi.org/10.1109/TCS.1975.1084079 (12) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  11. Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Springer, Waterloo, Canada (1983) (13) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  12. Hille, E., Tamarkin, J.D.: On a theorem of Paley and Wiener. Annals of Mathematics 34(3), 606–614 (1933) (14) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  13. Flanders, H.: Differentiation under the integral sign. The American Mathematical Monthly 80(6), 615–627 (1973). https://doi.org/10.2307/2319163 (15) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  14. Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1: The recovery technique. International Journal for Numerical Methods in Engineering 33(7), 1331–1364 (1992). https://doi.org/10.1002/nme.1620330702 (16) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  15. Keiter, E., Russo, T., Schiek, R., Thornquist, H., Mei, T., Verley, J., Aadithya, K., Schickling, J.: Xyce parallel electronic simulator reference guide, version 7.5. (2022) (17) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016) Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
  16. Keiter, E.R., Swiler, L.P., Russo, T.V., Wilcox, I.Z.: Sensitivity analysis in Xyce. (2016)
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