19 research outputs found

    The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids

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    Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For 3-D problems, only plane relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. A new multigrid algorithm is presented based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. This algorithm was developed and the standard multigrid theory was extended to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms. The algorithm described is a variant of Mulder's multigrid algorithm for hyperbolic problems. The latter uses multiple coarse grids to achieve robustness, but is unsuitable for elliptic problems, since its V-cycle convergence rate goes to one as the number of levels increases. The new algorithm combines the contributions from the multiple coarse grid via a local switch, based on the strength of the discrete operator in each coordinate direction

    A Semicoarsening Multigrid Algorithm for SIMD Machines

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    A semicoarsening multigrid algorithm suitable for use on single instruction multiple data (SIMD) architectures has been implemented on the CM-2. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance is compared with its performance on some other machines, both parallel and nonparallel

    Mapping implicit spectral methods to distributed memory architectures

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    Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case

    A Semicoarsening Multigrid Algorithm for SIMD Machines

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    Multigrid methods with applications to reservoir simulation

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    The Sixth Copper Mountain Conference on Multigrid Methods, part 2

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    The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth
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