Elliptic Marching Methods and Domain Decomposition

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Patrick J. Roache Richard Fateman (University of California, Berkeley, California, USA)

Elliptic Marching Methods and Domain Decomposition

Patrick J. Roache, Richard Fateman (University of California, Berkeley, California, USA)

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English

CRC Press Inc
29 June 1995

Differential calculus & equations; Numerical analysis; Mathematical theory of computation

Series: Symbolic & Numeric Computation

One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial

differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate

gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.

By: Patrick J. Roache
Series edited by: Richard Fateman (University of California Berkeley California USA)
Imprint: CRC Press Inc
Country of Publication: United States
Volume: 5
Dimensions: Height: 254mm, Width: 178mm, Spine: 16mm
Weight: 566g
ISBN: 9780849373787
ISBN 10: 0849373786
Series: Symbolic & Numeric Computation
Pages: 206
Publication Date: 29 June 1995
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

Basic Marching Methods for 2D Elliptic Problems High-Order Equations Extending the Mesh Size: Domain Decomposition Banded Approximations to Influence Matrices Marching Methods in 3D Performance of the 2D GEM Code Vectorization and Parallelization Semidirect Methods for Nonlinear Equations of Fluid Dynamics Comparison to Multigrid Methods Appendix A - Marching Schemes and Error Propagation for Various Discrete Laplacians Appendix B - Tridiagonal Algorithm for Periodic Boundary Conditions Appendix C - Gauss Elimination as a Direct Solver Subject Index TOC for NTI/Flyer

Patrick J. Roache

Reviews for Elliptic Marching Methods and Domain Decomposition

Together with an important historical perspective, this book uses the domain decomposition connection to develop and explore the nature of marching methods. Interesting analytical and anecdotal comparisons are made with direct methods and multigrid techniques, told by a scientist who has obviously has much experience with real practical problems. -Mathematical Reviews, 99a