Direct Schur complement method by domain decomposition based on -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
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35, 65F10
Keywords and phrases: domain decomposition, schur complement, $\mathcal{h}$-matrix approximation
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Abstract:
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 (-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost is almost linear in - the number of degrees of freedom on the interface. As input, we require the Schur complement matrices corresponding to subdomains and represented in the -matrix format. In the case of piecewise constant coefficients these matrices can be computed via the BEM representation with the cost , while in the general case the FEM discretisation leads to the complexity , where is the number of degrees of freedom in the domain.