This refereed volume arose from the editors' recognition that physical scientists, engineers, and applied mathematicians are developing, in parallel, solutions to problems of parallelization. The cross-disciplinary field of scientific computation is bringing about better communication between heterogeneous computational groups, as they face this common challenge. This volume is one attempt to provide cross-disciplinary communication. Problem decomposition and the use of domain-based parallelism in computational science and engineering was the subject addressed at a workshop held at the University of Minnesota Supercomputer Institute in April 1994. The authors were subsequently able to address the relationships between their individual applications and independently developed approaches. This book is written for an interdisciplinary audience and concentrates on transferable algorithmic techniques, rather than the scientific results themselves. Cross-disciplinary editing was employed to identify jargon that needed further explanation and to ensure provision of a brief scientific background for each chapter at a tutorial level so that the physical significance of the variables is clear and correspondences between fields are visible.
Chapter 1: A Family of Overlapping Schwarz Algorithms for Nonsymmetric and Indefinite Elliptic Problems, Xiao Chuan Cai Chapter 2: Domain Decomposition Methods for Wave Propagation Problems, Alfio Quarteroni Chapter 3: Domain Decomposition, Parallel Computing, and Petroleum Engineering, Petter Bjorstad and Terje Karstad Chapter 4: Parallel Implicit Methods for Aerodynamic Applications on Unstructured Grids, V. Venkatakrishnan Chapter 5: Newton Krylov Schwarz Methods Applied to the Tokamak Edge Plasma Fluid Equations, D.A. Knoll, P.R. McHugh, and V.A. Mousseau Chapter 6: Parallel Domain Decomposition Software, William Gropp and Barry Smith Chapter 7: Decomposition of Space Time Domains: Accelerated Waveform Methods, with Application to Semiconductor Device Simulation, Andrew Lumsdaine and Mark W. Reichelt Chapter 8: A Parallel Multi Level Solution Method for Large Markov Chains, Graham Horton Chapter 9: Optimizing Substructuring Methods for Repeated Right Hand Sides, Scalable Parallel Coarse Solvers, and Global/Local Analysis, Charbel Farhat Chapter 10: Parallel Implementation of a Domain Decomposition Method for Non Linear Elasticity Problems, Francois Xavier Roux Chapter 11: Fictitious Domain/Domain Decomposition Methods for Partial Differential Equations, Roland Glowinski, Tsorng Whay Pan, and Jacques Periaux Chapter 12: Multipole and Precorrected FFT Accelerated Iterative Methods for Solving Surface Integral Formulations of Three Dimensional Laplace Problems, K. Nabors, J. Phillips, F.T. Korsmeyer, and J. White Chapter 13: Linear Scaling Algorithms for Large Scale Electronic Structure Calculations, E.B. Stechel Chapter 14: Problem Decomposition in Quantum Chemistry, Hans Joachim Werner Chapter 15: Bound States of Strongly Coupled Multidimensional Molecular Hamiltonians by the Discrete Variable Representation Approach, Zlatko Bacic Chapter 16: Wave Operators and Active Subspaces: Tools for the Simplified Dynamical Description of Quantum Processes Involving Many Dimensional State Spaces, Georges Jolicard and John P. Killingbeck Chapter 17: Problem Decomposition Techniques in Quantum Mechanical Reactive Scattering, David W. Schwenke and Donald G. Truhlar.
