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• W1537835016 abstract "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-sparse format of $mathcal{H}$-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." @default.
• W1537835016 created "2016-06-24" @default.
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• W1537835016 date "2016-07-27" @default.
• W1537835016 modified "2023-09-26" @default.
• W1537835016 title "Existence of $mathscr{H}$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator" @default.
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• W1537835016 doi "https://doi.org/10.1093/imanum/drw024" @default.
• W1537835016 hasPublicationYear "2016" @default.
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