Preprint 25/2004

Direct Schur complement method by domain decomposition based on H-matrix approximation

Wolfgang Hackbusch, Boris N. Khoromskij, and Ronald Kriemann

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Submission date: 28. Apr. 2004
Pages: 16
published in: Computing and visualization in science, 8 (2005) 3/4, p. 179-188 
DOI number (of the published article): 10.1007/s00791-005-0008-3
MSC-Numbers: 65F30, 65F50, 65N35, 65F10
Keywords and phrases: domain decomposition, schur complement, $\mathcal{h}$-matrix approximation
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The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (formula23-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost formula25 is almost linear in formula27 - the number of degrees of freedom on the interface. As input, we require the Schur complement matrices corresponding to subdomains and represented in the formula23-matrix format. In the case of piecewise constant coefficients these matrices can be computed via the BEM representation with the cost formula25, while in the general case the FEM discretisation leads to the complexity formula33, where formula35 is the number of degrees of freedom in the domain.

03.07.2017, 01:40