218 RWTH Publication No: 47165        2002        IGPM2018.pdf
TITLE Compression Techniques for Boundary Integral Equations - Optimal Complexity Estimates
AUTHORS Wolfgang Dahmen, Helmut Harbrecht, Reinhold Schneider
ABSTRACT In this paper matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, that reduces the near field complexity significantly, and an additional a-posteriori compression. The latter one is based on a general result concerning an optimal work balance, that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time. The theoretical results are illustrated by a 3D example on a nontrivial domain.
KEYWORDS Wavelets, norm equivalences, multilevel preconditioning, first and second compression, a-posteriori compression, asymptotic complexity estimates
DOI 10.1137/S0036142903428852
PUBLICATION SIAM journal on numerical analysis
43(6), 2251-2271 (2006)