On Adaptive Wavelet Boundary Element Methods

Abstract

The present article is concerned with the numerical solution of boundary integral equations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution's best $N$-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geometries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.