Domain Decomposition Algorithms in the Mainstream of Computational Science
by David E. Keyes
Over the past two decades, domain decomposition has grown from an elegant mathematical technique to the dominant paradigm of large-scale scientific simulation for systems governed by partial differential equations. Two major families of domain decomposition methods -- Newton-Krylov-Schwarz (NKS) and Finite Element Tearing and Interconnecting (FETI) -- have been scalably employed on the ASCI platforms of the U.S. Department of Energy for mechanics problems, up to several thousand processors. This talk is intended as an overview of a wide range of issues in domain decomposition for scientific computing on distributed, hierarchical memory systems, including: algorithms, performance, programming paradigms, and illustrative applications. The algorithmic paradigms of Schwarz and Schur are considered, along with various hybrids, and their superiority in terms of data motion is noted relative to some standard decompositions. One of the scientific software projects intent on "packaging" the fruits of research in domain decomposition methods for mainstream computational scientists is a five-year, nine-institution "Terascale Optimal PDE Simulations Integrated Software Infrastructure Center", a component of DOE's new Scientific Discovery through Advanced Computing (SciDAC) initiative. The speaker, who serves as the TOPS project lead, will conclude by outlining the philosophy and goals of the center, and highlighting some of the research challenges ahead.