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Parallel multigrid methods. (English) Zbl 0865.65088

Keyes, David E. (ed.) et al., Parallel numerical algorithms. Proceedings of the workshop, Hampton, VA, May 23–25, 1994. Dordrecht: Kluwer Academic Publishers. ICASE/LaRC Interdisciplinary Series in Science and Engineering. 4, 203-224 (1997).
Summary: Multigrid methods have proved to be among the fastest numerical methods for solving a broad class of problems, from many types of partial differential equations to problems with no continuous origin. On a serial computer, multigrid methods are able to solve a widening class of problems with work equivalent to a few evaluations of the discrete residual (i.e., a few relaxations).
Many research projects have been conducted on parallel multigrid methods, and they have addressed a variety of subjects: from proposed new algorithms to theoretical studies to questions about practical implementation. The aim here is to provide a brief overview of this active and abundant field of research, with the aim of providing some guidance to those who contemplate entering it.
For the entire collection see [Zbl 0857.00034].

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
65N06 Finite difference methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation
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