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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Approximation of Integral Operators by Variable-Order Interpolation
Jens Markus Melenk, Steffen Börm and Maike LöhndorfAbstract
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.
- Received:
- 09.09.02
- Published:
- 09.09.02
- MSC Codes:
- 45B05, 65N38, 68P05
- Keywords:
- hierarchical matrices, bem, fast matrix-vector multiplication