Fast multipole boundary element method for the Laplace equation in a locally perturbed half-plane with a Robin boundary condition
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Date
2012
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Abstract
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. (C) 2012 Elsevier B.V. All rights reserved.
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Keywords
Laplace equation, Robin boundary condition, Fast multipole algorithm, Boundary element method, Exponential integral function