Accelerating Galerkin BEM for Linear Elasticity using Adaptive Cross Approximation
Mario Bebendorf and Richard Grzibovski
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Submission date: 02. May. 2006
published in: Mathematical methods in the applied sciences, 29 (2006) 14, p. 1721-1747
DOI number (of the published article): 10.1002/mma.759
MSC-Numbers: 65D05, 65D15, 65F05
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The adaptive cross approximation (ACA) algorithm provides a means to compute data-sparse approximants of discrete integral formulations of elliptic boundary value problems with almost linear complexity. ACA uses only few of the original entries for the approximation of the whole matrix and is therefore well-suited to speed up existing computer codes. In this article we extend the convergence proof of ACA to Galerkin discretizations. Additionally, we prove that ACA can be applied to integral formulations of systems of second-order elliptic operators without adaptation to the respective problem. The results of applying ACA to boundary integral formulations of linear elasticity are reported. Furthermore, we comment on recent implementation issues of ACA for nonsmooth boundaries.