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MiS Preprint

Approximation of Integral Operators by Variable-Order Interpolation

Jens Markus Melenk, Steffen Börm and Maike Löhndorf


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.

MSC Codes:
45B05, 65N38, 68P05
hierarchical matrices, bem, fast matrix-vector multiplication

Related publications

2005 Repository Open Access
Steffen Börm, Maike Löhndorf and Jens Markus Melenk

Approximation of integral operators by variable-order interpolation

In: Numerische Mathematik, 99 (2005) 4, pp. 605-643