Fast multipole boundary element method for the Laplace equation in a locally perturbed half-plane with a Robin boundary condition

A fast multipole boundary element method (FM-BEM) for solving large-scale potential problems ruled by the Laplace equation in a locally-perturbed 2-D half-plane with a Robin boundary condition is developed in this paper. These problems arise in a wide gamut of applications, being the most relevant one the scattering of water-waves by floating and submerged bodies in water of infinite depth. The method is based on a multipole expansion of an explicit representation of the associated Green’s function, which depends on a combination of complex-valued exponential integrals and elementary functions. The resulting method exhibits a computational performance and memory requirements similar to the classic FM-BEM for full-plane potential problems. Numerical examples demonstrate the accuracy and efficiency of the method.

► A FM-BEM for the Laplace equation in half-plane with Robin condition is developed.
► We perform a suitable expansion of the exponential integral function.
► Error bounds for the truncated series expansions are obtained.
► Numerical examples show the accuracy and performance of the proposed method.