Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions: January 1991 (Classic Reprint) - Softcover
Synopsis
Efficient, parallel methods for solving Poisson's and biharmonic equations on irregular regions.
This book explains how integral equation formulations coupled with fast finite difference solvers can tackle large, complex problems while staying well suited to parallel computing.
The text describes a unified approach that embeds an irregular region in a larger rectangle and uses dense, well‑conditioned systems solved by iterative methods. It covers how to compute boundary discontinuities, apply fast Poisson solvers, and obtain accurate derivatives directly. The discussion emphasizes practical parallel and vectorizable algorithms that work on exterior regions and complex geometries.
Readers will see concrete comparisons of iterative methods, learn how to implement them on parallel hardware, and review numerical experiments across multiple platforms. The work highlights performance considerations, accuracy, and the tradeoffs involved in choosing solvers for large, dense systems arising from integral equation formulations.
- How to embed irregular regions for efficient computation and boundary handling
- How integral equations pair with fast Poisson solvers to solve PDEs
- How different iterative methods perform on dense, non-symmetric systems
- Practical guidance on parallel and vector implementation for large-scale problems
Ideal for readers of computational mathematics and parallel numerical analysis seeking practical, experiment-backed methods.
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Paperback. Condition: New. Print on Demand. This book introduces a novel method for solving Poisson's and the biharmonic equations on irregular regions. Using integral equations and iterative numerical methods, the author explores an alternative to standard approaches, which often rely on finite element methods that can be time-consuming and computationally expensive. The book presents a detailed examination of the well-conditioned integral equation formulations and iterative methods used to solve the dense nonsymmetric linear systems that arise from the integral equations. The author includes numerical experiments conducted on a variety of parallel and vector supercomputers, demonstrating the efficiency and accuracy of the presented methods. This book is a valuable resource for researchers and practitioners in computational science, engineering, and applied mathematics, offering a deeper understanding of integral equation formulations and iterative methods for solving partial differential equations on irregular regions. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332127177_0
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Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions January 1991 Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332127177
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Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions January 1991 Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332127177
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