Titlebook: Matrix-Based Multigrid; Theory and Applicati Yair Shapira Textbook 2008Latest edition Springer-Verlag US 2008 Helmholtz equation.computer.c

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Matrix-Based Multigrid978-0-387-49765-5Series ISSN 1571-5698

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The Multilevel-Multiscale ApproachIn this chapter, we describe the concept of multilevel and multiscale, and use them in several elementary examples: from basic algorithms in arithmetics of integer numbers, through mathematical induction and recursion, to data structures and parallel algorithms.

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PreliminariesIn this chapter, we list some basic definitions and prove some standard lemmas used throughout the book. In particular, the lemmas are used to obtain some useful properties of the one- and two-dimensional Fourier (sine) transform, which are used often in the book.

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Iterative Linear System SolversIn this chapter, we present several iterative methods for the solution of large sparse linear systems of algebraic equations. We start with relaxation methods such as point and block Jacobi and Gauss–Seidel (GS) and Kacmarz versions, proceed to conjugate-gradient type acceleration methods, and conclude with incomplete LU (ILU) versions.

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Matrix-Based Semicoarsening MethodIn this chapter, we describe in detail the matrix-based multigrid method that uses semicoarsening (Section 6.11). In particular, we show how this method can be obtained as an interesting combination of domain decomposition, line-ILU, and variational multigrid.

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Textbook 2008Latest editionor courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered,? the only prerequisites are elementary linear algebra and calculus....Excerpts from the reviews of the fi

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n und aus dem Bereich des Internet. Zus?tzlich wurde als Unterstützung eine Webseite eingerichtet, die es den Studierenden erm?glicht, interaktiv und mit L?sungshilfen die übungsaufgaben des Bu978-3-540-30316-9978-3-540-30318-3Series ISSN 1614-5216