Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2011.10073v2)

Abstract: In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed "behind-the-scenes," with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.

• The paper introduces a unified solver interface and an object-oriented redesign that simplify integration with external libraries.
• It enhances vector operations with fused and many-vector capabilities to improve performance on modern hardware.
• It modernizes Fortran interfaces, offering improved compatibility and efficiency for high-performance computing simulations.

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers

This scholarly article presents a comprehensive redesign of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) libraries, stressing adaptability to application-specific and third-party algebraic solvers and data structures. The authors, Gardner et al., meticulously restructured various components of SUNDIALS to bolster flexibility, efficiency, and ease of integration with external libraries.

Key Innovations and Enhancements

The authors pursued several primary goals in this rigorous redesign:

1. Unified Solver Interfaces: The formulation of a single, consistent interface for linear solvers streamlines integration and reduces redundant code. Historically, each solver had distinct interface implementations across SUNDIALS packages. The new SUNLinearSolver class consolidates these into a unified interface that maximizes code reuse and compatibility.
2. Object-Oriented Design: Incorporating the object-oriented paradigm into the core class implementations—N_Vector, SUNMatrix, SUNLinearSolver, and SUNNonlinearSolver—ensures that the specific details of data layouts and solvers are encapsulated within abstract class definitions. This encapsulation significantly enhances the interoperability of SUNDIALS with customized data structures and solvers from other libraries.
3. Flexible Vector Operations: The N_Vector class was expanded, introducing new "fused" operations that consolidate multiple vector operations into a single call, thereby improving performance on modern hardware architectures. Additionally, the "many-vector" concept allows the combination of different vector instances into a single entity, enabling efficient use of heterogeneous hardware.
4. Fortran 2003 Interfaces: Replacing the outdated Fortran 77 interfaces, the new Fortran 2003 interfaces leverage features from the updated Fortran standard to ensure better compatibility and sustainability. This upgrade provides Fortran users with access to the full suite of SUNDIALS features and more straightforward interfacing with modern Fortran applications.

Numerical and Practical Implications

The enhancements described fortify SUNDIALS with the flexibility to better handle the advancing complexity of scientific simulations and the evolving landscape of high-performance computing (HPC) systems. The introduction of the many-vector capability, in particular, is anticipated to have substantial implications for multiphysics simulations and heterogeneous computing environments.

Comparative Performance and Use Cases

The article highlights two critical demonstration problems that showcase the practical benefits of the new flexibility:

1. 2D Heat Equation: Comparisons between various integrator and solver combinations revealed that the new infrastructure does not increase computational overhead and enables swift comparisons across different solvers, allowing users to identify the best tool for their specific application.
2. 1D Advection-Reaction Problem: Utilizing custom nonlinear solvers optimized for localized computations significantly reduced computational costs and synchronization overhead, illustrating the potential for substantial performance gains through problem-specific solver designs.

Future Directions

The revised SUNDIALS architecture lays a solid foundation for future developments:

• Enhanced On-Node Parallelism: Development of new vector and matrix classes to leverage diverse on-node parallelism approaches aims to further optimize computational performance on heterogeneous hardware.
• Reduced Communication Algorithms: The introduction of fused operations paves the way for research into algorithms that minimize communication overhead, which can drastically improve performance in distributed computing environments.
• Expanded Solver Interfaces: Continued expansion of native solver interfaces will enhance collaboration with a broader range of numerical libraries, fostering an ecosystem where SUNDIALS acts as a pivotal integration point for advanced computational problems.

Conclusion

The substantial restructuring of the SUNDIALS suite detailed in this paper results in a markedly more flexible, efficient, and sustainable set of tools for solving differential/algebraic equations and nonlinear systems. Its object-oriented design, unified solver interfaces, enhanced vector capabilities, and modern Fortran interfaces collectively represent a significant leap forward in numerical software engineering tailored for contemporary and future HPC challenges. As computational demands grow, these improvements equip SUNDIALS to remain a vital resource for researchers and practitioners in the field.