Elliptic marching methods and domain decomposition
著者
書誌事項
Elliptic marching methods and domain decomposition
（Symbolic and numeric computation series）
CRC Press, c1995
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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
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