Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation

The adaptive cross approximation (ACA) algorithm (Numer. Math. 2000; 86:565-589; Computing 2003; 70(1):1-24) 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 non-smooth boundaries.