Multigrid transfers for nonsymmetric systems based on Schur complements and Galerkin projections |
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Authors: | T A Wiesner R S Tuminaro W A Wall M W Gee |
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Institution: | 1. Institute for Computational Mechanics, Technische Universit?t München, , Boltzmannstr. 15, 85748 Garching, Germany;2. Sandia National Laboratories, PO Box 969, MS 9159, Livermore, CA 94551, U.S.A.;3. Mechanics and High Performance Computing Group, Technische Universit?t München, , Boltzmannstr. 15, 85748 Garching, Germany |
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Abstract: | A framework is proposed for constructing algebraic multigrid transfer operators suitable for nonsymmetric positive definite linear systems. This framework follows a Schur complement perspective as this is suitable for both symmetric and nonsymmetric systems. In particular, a connection between algebraic multigrid and approximate block factorizations is explored. This connection demonstrates that the convergence rate of a two‐level model multigrid iteration is completely governed by how well the coarse discretization approximates a Schur complement operator. The new grid transfer algorithm is then based on computing a Schur complement but restricting the solution space of the corresponding grid transfers in a Galerkin‐style so that a far less expensive approximation is obtained. The final algorithm corresponds to a Richardson‐type iteration that is used to improve a simple initial prolongator or a simple initial restrictor. Numerical results are presented illustrating the performance of the resulting algebraic multigrid method on highly nonsymmetric systems. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | algebraic multigrid Schur complement Galerkin projection nonsymmetric problems |
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