Lagrange Multiplier Based Substructuring: FETI Method
In this chapter, we describe the FETI method (the Finite Element Tearing and Interconnecting method) [FA2, FA16, FA15, MA25, FA14, KL8]. It is a Lagrange multiplier based iterative substructuring method for solving a finite element discretization of a sel
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Tarek P. A. Mathew
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations With 40 Figures and 1 Table
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Tarek Poonithara Abraham Mathew [email protected]
ISBN 978-3-540-77205-7
e-ISBN 978-3-540-77209-5
Lecture Notes in Computational Science and Engineering ISSN 1439-7358 Library of Congress Control Number: 2008921994 Mathematics Subject Classification (2000): 65F10, 65F15, 65N22, 65N30, 65N55, 65M15, 65M55, 65K10 c 2008 Springer-Verlag Berlin Heidelberg
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In loving dedication to my (late) dear mother, and to my dear father and brother
Preface
These notes serve as an introduction to a subject of study in computational mathematics referred to as domain decomposition methods. It concerns divide and conquer methods for the numerical solution and approximation of partial differential equations, primarily of elliptic or parabolic type. The methods in this family include iterative algorithms for the solution of partial differential equations, techniques for the discretization of partial differential equations on non-matching grids, and techniques for the heterogeneous approximation of partial differential equations of heterogeneous character. The divide and conquer methodology used is based on a decomposition of the domain of the partial differential equation into smaller subdomains, and by design is suited for implementation on parallel computer architectures. However, even on serial computers, these methods can provide flexibility in the treatment of complex geometry and heterogeneities in a partial differential equation. Interest in this family of computational methods for partial differential equations was spawned following the development of various high performance multiprocessor computer architectures in the early eighties. On such parallel computer architectures, the execution time of these algorithms, as well as the memory requirements per processor, scale reasonably well with the size of the problem and the number of processors. From a computational viewpoint, the divide and conquer methodology based on a decomposition of the domai
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