Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions: January 1991 (Classic Reprint) - Tapa blanda
Sinopsis
Excerpt from Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions: January 1991
The methods presented here combine integral equation formulations of the problems with rapid finite difference methods on a larger rectangular region in which the irregular region is embedded. Both the integral equation method and the finite difference method parallelize and vectorize well. By using well-conditioned integral equation formulations and iterative methods for solving them, the main part of the computation is reduced to the iterative solution of a dense nonsymmetric matrix equation, instead of a (much larger) sparse (although symmetric) system of equations with an irregular pattern of nonzero elements.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Reseña del editor
Excerpt from Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions: January 1991
The methods presented here combine integral equation formulations of the problems with rapid finite difference methods on a larger rectangular region in which the irregular region is embedded. Both the integral equation method and the finite difference method parallelize and vectorize well. By using well-conditioned integral equation formulations and iterative methods for solving them, the main part of the computation is reduced to the iterative solution of a dense nonsymmetric matrix equation, instead of a (much larger) sparse (although symmetric) system of equations with an irregular pattern of nonzero elements.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions: January 1991
In [10] a method was introduced for solving Poisson's or the biharmonic equation on an irregular region by making use of an integral equation formulation. Because fast solvers were used to extend the solution to an enclosing rectangle, this method avoided many of the standard problems associated with integral equations. The equations that arose were Fredholm integral equations of the second kind with bounded kernels. In this paper we use iterative methods to solve the dense nonsymmetric linear systems arising from the integral equations. Because the matrices are very well-conditioned, conjugate gradient-like methods can be used and will converge very rapidly. The methods are very amenable to vectorization and parallelization, and we describe parallel and vector implementations on shared memory multiprocessors. Numerical experiments are described and results presented for a 3-dimensional interface problem for the Laplacian on a recording head geometry.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Paperback. Condición: 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. Nº de ref. del artículo: 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. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332127177
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Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions January 1991 Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332127177
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