Robust Multigrid Methods (Notes on Numerical Fluid Mechanics): Proceedings of the Fourth GAMM-Seminar, Kiel, January 22 to 24,1988: 23 (Notes on ... Mechanics and Multidisciplinary Design, 23) - Tapa blanda

Hackbusch, Wolfgang

 
9783528080976: Robust Multigrid Methods (Notes on Numerical Fluid Mechanics): Proceedings of the Fourth GAMM-Seminar, Kiel, January 22 to 24,1988: 23 (Notes on ... Mechanics and Multidisciplinary Design, 23)
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ISBN 10: 3528080973 ISBN 13: 9783528080976
Editorial: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1989

Sinopsis

In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec­ tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.

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Reseña del editor

In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec­ tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.

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Editorial
Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
Año de publicación
1989
Idioma
Alemán
ISBN 10 
3528080973
ISBN 13 
9783528080976
Encuadernación
Tapa blanda
Número de páginas
256
Contacto del fabricante
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