²-matrices — Multilevel methods for the approximation of integral operators

Steffen Börm

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Submission date: 31. Jan. 2003
Pages: 20
published in: Computing and visualization in science, 7 (2004) 3/4, p. 173-181 
DOI number (of the published article): 10.1007/s00791-004-0135-2
Bibtex
MSC-Numbers: 65F30, 65N38
Keywords and phrases: bem, data-sparse approximations, hierarchical matrices
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Abstract:

Multigrid methods are typically used to solve partial differential equations, i.e., they approximate the inverse of the corresponding partial differential operators. At least for elliptic PDEs, this inverse can be expressed in the form of an integral operator by Green's theorem.

This implies that multigrid methods approximate certain integral operators, so it is straightforward to look for variants of multigrid methods that can be used to approximate more general integral operators.

-matrices combine a multigrid-like structure with ideas from panel clustering algorithms in order to provide a very efficient method for discretizing and evaluating the integral operators found, e.g., in boundary element applications.