M. Faustmann, J. Melenk, D. Praetorius:

"Existence of $\cal H$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator";

in: "ASC Report 08/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 30.

We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank

matrices at an exponential rate in the block rank. We cover in particular the data-space format of $\cal H$-matrices. We show the approximability result for two types of discretizations. The first one is a saddle point formulation, which incorporates the constraint of vanishing mean of the solution. The second discretization is based on a stabilized hyper-singular operator, which leads to symmetric

positive definite matrices. In this latter setting, we also show that the hierarchical Cholesky factorization can be approximated at an exponential rate in the block rank.

http://www.asc.tuwien.ac.at/preprint/2015/asc08x2015.pdf

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