ICCS 2007 : Keynote Abstract Keyes

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 PDE Simulations ( 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, quantum chromodynamics, and subsurface flows. We then describe the algorithmic and software roadmap of TOPS, which includes such well-known packages as Hypre, PETSc, ScaLAPACK, SUNDIALS, SuperLU, and Trilinos.

David E. Keyes is the Fu Foundation Professor of Applied Mathematics in the Department of Applied Physics and Applied Mathematics at Columbia University, an affiliate of the Center for Computational Science (CSC) at Brookhaven National Laboratory, and Acting Director of Institute for Scientific Computing Research (ISCR) at the Lawrence Livermore National Laboratory. Keyes graduated summa cum laude with a B.S.E. in Aerospace and Mechanical Sciences and a Certificate in Engineering Physics from Princeton University in 1978. He received his Ph.D. in Applied Mathematics from Harvard University in 1984. He then post-doc'ed in the Computer Science Department at Yale University and taught there for eight years, as Assistant and then Associate Professor of Mechanical Engineering, prior to joining Old Dominion University and the Institute for Computer Applications in Science & Engineering (ICASE) at the NASA Langley Research Center in 1993.

Keyes is the author or co-author of over 100 publications in computational science and engineering, numerical analysis, and computer science. He has co-edited 8 conference proceedings concerned with parallel algorithms and has delivered over 200 invited presentations at universities, laboratories, and industrial research centers in over 20 countries and 35 states of the U.S. With backgrounds in engineering, applied mathematics, and computer science, and consulting experience with industry and national laboratories, Keyes works at the algorithmic interface between parallel computing and the numerical analysis of partial differential equations, across a spectrum of aerodynamic, geophysical, and chemically reacting flows. Newton-Krylov-Schwarz parallel implicit methods, introduced in a 1993 paper he co-authored at ICASE, are now widely used throughout engineering and computational physics, and have been scaled to thousands of processors on the ASCI platforms. Keyes has co-organized and lectured in numerous conferences and short courses on high-performance computing for systems modeled by PDEs for NASA Langley, LLNL, SIAM, the DoD Modernization Centers, the domain decomposition and parallel CFD communities, and university departments. He is currently co-editor of Int J High Performance Computing Applications and Springer's Lecture Notes in Computational Science & Engineering and has served as an editorial board member of SIAM J Scientific Computing.