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- Title
Parameter-free H(div) preconditioning for a mixed finite element formulation of diffusion problems.
- Authors
Powell, Catherine E.
- Abstract
Mixed finite element formulations of generalised diffusion problems yield linear systems with ill-conditioned, symmetric and indefinite coefficient matrices. Preconditioners with optimal work complexity that do not rely on artificial parameters are essential. We implement lowest order Raviart–Thomas elements and analyse practical issues associated with so-called ‘H(div) preconditioning’. Properties of the exact scheme are discussed in Powell & Silvester (2003, SIAM J. Matrix Anal. Appl., 25, 718–738). We extend the discussion, here, to practical implementation, the components of which are any available multilevel solver for a weighted H(div) operator and a pressure mass matrix. A new bound is established for the eigenvalue spectrum of the preconditioned system matrix and extensive numerical results are presented.
- Subjects
FINITE element method; MATRICES (Mathematics); ABSTRACT algebra; NUMERICAL analysis; MATHEMATICAL analysis
- Publication
IMA Journal of Numerical Analysis, 2005, Vol 25, Issue 4, p783
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/dri017