Description
Book SynopsisOne 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 mathem
Trade Review"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
Table of ContentsBasic 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
