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Block-Adaptive Cross Approximation of Discrete Integral Operators

Maximilian Bauer and Mario Bebendorf


In this article, we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical matrix approximations having the same prescribed accuracy on all blocks of the partition, for the solution of linear systems, it may be more efficient to adapt the accuracy of each block to the actual error of the solution as some blocks may be more important for the solution error than others. To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the blockwise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution.

MSC 2010: 65N38

Funding source: Deutsche Forschungsgemeinschaft

Award Identifier / Grant number: BE2626/4-1

Funding statement: This work was supported by the DFG project BE2626/4-1.


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Received: 2019-05-13
Revised: 2019-12-30
Accepted: 2020-01-13
Published Online: 2020-02-05
Published in Print: 2021-01-01

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