Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
129 tokens/sec
GPT-4o
28 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Global convergence of iterative solvers for problems of nonlinear magnetostatics (2403.18520v1)

Published 27 Mar 2024 in math.NA and cs.NA

Abstract: We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the damped Newton-method, fixed-point iteration, and the Kacanov iteration, which can all be interpreted as generalized gradient descent methods. Armijo backtracking isconsidered for an adaptive choice of the stepsize. The general assumptions required for our analysis cover inhomogeneous, nonlinear, and anisotropic materials, as well as permanent magnets. The main results are proven on the continuous level, but they carry over almost verbatim to various approximation schemes, including finite elements and isogeometric analysis, leading to bounds on the iteration numbers, which are independent of the particular discretization. The theoretical results are illustrated by numerical tests for a typical benchmark problem.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (16)
  1. Meunier, G.: The Finite Element Method for Electromagnetic Modeling. ISTE Wiley (2008)
  2. IEEE Trans. Magn. 27, 3804–3807 (1991)
  3. IEEE Trans. Magn. 44, 473–478 (2008)
  4. IEEE Trans. Magn. 41, 1724–1727 (2005)
  5. IEEE Trans. Magn. 40, 1076–1079 (2004)
  6. Math. Comput. Appl. 24, art.nr. 19 (2019)
  7. Appl. Numer. Math. 24, 57–79 (1997)
  8. Springer, New York, NY, USA (2006)
  9. Heid, P.: A short note on an adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations. Arch. Math. 121, 55–65 (2023)
  10. Engertsberger, F.: The scalar potential approach in nonlinear magnetostatics. Master’s thesis, Johannes Kepler University Linz (2023)
  11. Monk, P.: Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003)
  12. Springer (1990)
  13. Heise, B.: Analysis of a fully discrete finite element method for a nonlinear magnetic field problem. SIAM J. Numer. Anal. 31, 745–759 (1994)
  14. IEEE Trans. Appl. Supercond. 30, 1–13 (2020)
  15. TEAM benchmark problems. URL https://www.compumag.org/wp/team
  16. J. Comp. Appl. Math. 196, 45–57 (2006)
Citations (1)

Summary

We haven't generated a summary for this paper yet.