Scalable Solvers and Software for PDE-based Applications

Prof. David E. Keyes

Abstract: Like the theoretical peak performance of a computer system, theoretical efficiency for algorithms is rarely closely approached for real applications. While the quest for the "textbook efficiency" continues on many fronts, applications scientists need to have their solver capabilities upgraded today to exploit the platform potential to run more highly resolved computations. The Terascale Optimal PDE Simulations (TOPS) project of the Scientific Discovery through Advanced Computing (SciDAC) initiative is working on both fronts---attempting to make fundamental advances in numerical algorithms that will be integrated into tomorrow's scalable solver software while achieving gains for SciDAC application developers at the outset of the initiative.

This talk dwells on some practical aspects of migrating from a legacy (usually operator-split) nonlinear solver for evolutionary or equilibrium systems of PDEs to a Jacobian-free Newton-Krylov framework that provides strong controls on splitting error while still incorporating physically-based operator-split methodology (and even legacy subroutines) where possible. It is emphasized that to support even a single application from development through production use on various platforms, contemporary solver libraries must offer a menu of flexibility combinable and tunable components to allow application-specific and architecture-specific trade-offs (e.g., memory versus flops, synchronization frequency versus stability, robustness versus efficiency). We also discuss some experiences with DOE's M3D extended magnetohydrodynamics code, which is designed to underscore the desirability of being able to draw from a broad family of solvers within a single application.