Scalable Solver Infrastructure for Computational Science & Engineering

Multiscale, multirate scientific and engineering applications based on systems of partial differential equations possess resolution requirements that demand execution on the highest-capability computers available, which will soon reach the petascale. While the variety of applications is enormous, their needs for mathematical software infrastructure are surprisingly coincident. Implicit methods for transient and equilibrium problems lead after discretization to large, ill-conditioned algebraic systems. The chief to bottleneck to scalability is often the solver. At their current scalability limits, many applications spend a vast majority of their operations in solvers, due to solver algorithmic complexity that is superlinear in the problem size, whereas other phases scale linearly. Furthermore, the solver may be the phase of the simulation with the poorest parallel scalability, due to intrinsic global dependencies. The Towards Optimal Petascale Simulations (TOPS, www.scidac.gov/math/TOPS.html) project focuses on ameliorating this bottleneck while providing a multilevel programming interface that allows users to advance from initial concerns of correctness and robustness to ultimate concerns of efficiency and performance portability by experimenting with a variety of solvers. We begin with an overview of the diverse petascale hardware roadmaps at the laboratories served by the TOPS project, with such applications as electromagnetism, magnetohydrodynamics, and quantum chromodynamics. We then describe the algorithmic and software roadmap of TOPS, which includes such well-known packages as Hypre, PETSc, SUNDIALS, SuperLU, and Trilinos.