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DOI 10.5286/raltr.2008003
Persistent URL http://purl.org/net/epubs/work/56171
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Record Id 56171
Title Matrix square-root preconditioners for the Steklov-Poincare operator
Abstract A key computational ingredient in domain decomposition methods for scalar elliptic problems is the preconditioning of a discrete Steklov-Poincare operator defined on the union of the boundaries of each subdomain. This operator is norm-equivalent to a discrete fractional Sobolev norm-matrix of index 1/2. This norm-matrix is related to the matrix square-root of a certain generalised Laplacian operator defined on the subdomain boundaries. In this work we introduce a Krylov subspace approach to approximate the action of the inverse of such a norm-matrix in a sparse fashion. The resulting algorithm is shown to be optimal for preconditioning domain decomposition methods for elliptic problems. Numerical experiments demonstrate that it is also quasi-scalable.
Organisation CSE , CSE-NAG , STFC
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-003. 2008. arlo2008003.pdf 2008