A Black-Box Multigrid Preconditioner for the Biharmonic Equation

Authors: Silvester D.J.¹; Mihajlovi cacute M.D.²

Source: Bit Numerical Mathematics, Volume 44, Number 1, 2004 , pp. 151-163(13)

Publisher: Springer

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Abstract:

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.

Keywords: biharmonic equation; mixed methods; finite elements; preconditioning; multigrid

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:BITN.0000025094.68655.c7

Affiliations: 1: Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester M60 1QD, UK., Email: na.silvester@na-net.ornl.gov 2: Department of Computer Science, University of Manchester, Oxford Road, Manchester M13 9PL, UK., Email: milan@cs.man.ac.uk

Publication date: 2004-01-01