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Domain decomposition methods for the numerical solution of partial differential equations

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Published by Springer in Berlin .
Written in English

Subjects:

  • Decomposition method,
  • Differential equations, Partial -- Numerical solutions

Book details:

Edition Notes

Includes bibliographical references (p. [711]-760) and index.

StatementTarek P.A. Mathew.
SeriesLecture notes in computational science and engineering -- 61
Classifications
LC ClassificationsQA402.2 .M38 2008
The Physical Object
Paginationxiii, 764 p. :
Number of Pages764
ID Numbers
Open LibraryOL17041209M
ISBN 103540772057, 354077209X
ISBN 109783540772057, 9783540772095
LC Control Number2008921994

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Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and . Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations Tarek Poonithara Abraham Mathew In this chapter, we describe iterative methods for solving the. A relatively new field, domain composition methods draw on parallel computing techniques and are proving a powerful approach to the numerical solution of partial differential equations. This book. Domain decomposition methods are designed to allow the effective numerical solution of partial differential equations on parallel computer architectures. They comprise a relatively new field of study but have already found important applications in many branches of physics and engineering. In this book the authors illustrate the basic mathematical concepts behind domain decomposition, looking.

"Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations. Abstract Domain decomposition methods are iterative methods for the solution of linear or nonlinear systems that use explicit information about the geometry, discretization, and/or partial differential equations that underlie the discrete by: Much of the work on domain decomposition has been directed at elliptic equations (see, for example, [1, 2, 4, 6] and the references therein). Such al-gorithms could quite easily be applied to parabolic equations, giving domain decomposition iterative methods for the solution of the equations .   Abstract Domain decomposition refers to divide and conquer techniques for solving partial differential equations by iteratively solving subproblems defined on smaller subdomains. The principal advantages include enhancement of parallelism and localized treatment of complex and irregular geometries, singularities and anomalous regions.

According to a general theory of domain decomposition methods (DDM), recently proposed by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz‐Herrera methods). This article is devoted to formulate systematically indirect methods and apply them to differential equations in several dimensions.   A two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that the condition number of the preconditioned system is bounded by C (1 + H / δ), where H is the maximum diameter of subdomains. S. Ushijima, I. Nezu, in Parallel Computational Fluid Dynamics , 2 INTRODUCTION. Domain decomposition methods with the parallel numerical procedures are effective techniques to solve many types of large scale discretized equations [1], [2].In this study, in order to develop a fast and accurate computational method for advection-diffusion equations, a fifth-order QSI (quintic.   () Solution domain decomposition with finite difference methods for partial differential equations. Numerical Methods for Partial Differential Equations , Mo Mu.