MiS Preprint Repository

The present paper introduces an $hp$-version of BEM for the Laplace equation in polyhedral domains based on meshes which are concentrated to zones on the surface (wire-basket zones), where the regularity of the solution is expected to be low. For the classical boundary integral equations, we prove the optimal approximation results and discuss the stability aspects. Then, we construct the panel-clustering and $\mathcal{H}$-matrix approximations to the corresponding Galerkin BEM stiffness matrix and prove their linear-logarithmic cost. The method is shown to have an almost linear complexity with respect to the number of degrees of freedom located on the wire basket.