A Black-Box Multigrid Preconditioner for the Biharmonic Equation

Silvester, David and Mihajlovic, Milan D. (2004) A Black-Box Multigrid Preconditioner for the Biharmonic Equation. BIT Numerical Mathematics, 44 (1). pp. 151-163. ISSN 1572-9125

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We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditioned systems having an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. Numerical results show that the performance of the methodology is competitive with that of specialized fast iteration methods that have been developed in the context of biharmonic problems.

Item Type: Article
Uncontrolled Keywords: biharmonic equation - mixed methods - finite elements - preconditioning - multigrid
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 26 Oct 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/633

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