The nested recursive two-level factorization method for nine-point difference matrices
Nested recursive two-level factorization methods for nine-point difference matrices are analyzed. Somewhat similar in construction to multilevel methods for finite element matrices, these methods use recursive red-black orderings of the meshes, approximating the nine-point stencils by five-point one...
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Published in | SIAM journal on scientific and statistical computing Vol. 12; no. 6; pp. 1373 - 1400 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.11.1991
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Subjects | |
Online Access | Get full text |
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Summary: | Nested recursive two-level factorization methods for nine-point difference matrices are analyzed. Somewhat similar in construction to multilevel methods for finite element matrices, these methods use recursive red-black orderings of the meshes, approximating the nine-point stencils by five-point ones in the red points and then forming the reduced system explicitly. Because this Schur complement is again a nine-point matrix (on a skew grid this time), the process of approximating and factorizing can be applied anew. Progressing until a sufficiently coarse grid has been reached, this procedure gives a multilevel preconditioner for the original matrix. Solving the levels in $V$-cycle order will not give an optimal order method (that is, with a total work proportional to the number of unknowns), but we show that using certain combinations of $V$-cycles and $W$-cycles will give methods of both optimal order of numbers of iterations and computational complexity. Since all systems to be solved during a preconditioner solve are of diagonal form, the method is suitable for execution on massively parallel architectures. |
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ISSN: | 0196-5204 1064-8275 2168-3417 1095-7197 |
DOI: | 10.1137/0912075 |