Approximation of Integral Operators by Variable-Order Interpolation
Jens Markus Melenk, Steffen Börm, and Maike Löhndorf
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Submission date: 09. Sep. 2002 (revised version: June 2004)
published in: Numerische Mathematik, 99 (2005) 4, p. 605-643
DOI number (of the published article): 10.1007/s00211-004-0564-3
MSC-Numbers: 45B05, 65N38, 68P05
Keywords and phrases: hierarchical matrices, bem, fast matrix-vector multiplication
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We employ a data-sparse, recursive matrix representation, so-called H2-matrices, for the efficient treatment of discretized integral operators. The format is obtained using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones.
The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators mapping L2 to L2. In particular, we show that the optimal convergence O(h) is retained for the classical double layer potential discretized with piecewise constant functions.