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.
%0 Journal Article
%1 prezarancibia2012multipole
%A Pérez-Arancibia, Carlos
%A Ramaciotti, Pedro
%A Hein, Ricardo
%A Durán, Mario
%D 2012
%J Computer Methods in Applied Mechanics and Engineering
%K 35j05-laplacian-operator-helmholtz-poisson-equation 35j08-pdes-elliptic-greens-functions 65n38-boundary-element-methods
%P 152-163
%R 10.1016/j.cma.2012.04.012
%T Fast multipole boundary element method for the Laplace equation in a locally perturbed half-plane with a Robin boundary condition
%U https://www.sciencedirect.com/science/article/pii/S0045782512001326
%V 233-236
%X 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.
@article{prezarancibia2012multipole,
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.},
added-at = {2021-04-16T02:31:49.000+0200},
author = {Pérez-Arancibia, Carlos and Ramaciotti, Pedro and Hein, Ricardo and Durán, Mario},
biburl = {https://www.bibsonomy.org/bibtex/23017afd5cc3b4457db9c64a78fd6bbc7/gdmcbain},
doi = {10.1016/j.cma.2012.04.012},
interhash = {3cf5bd47ff19034d4f96ad4c9a533842},
intrahash = {3017afd5cc3b4457db9c64a78fd6bbc7},
issn = {0045-7825},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {35j05-laplacian-operator-helmholtz-poisson-equation 35j08-pdes-elliptic-greens-functions 65n38-boundary-element-methods},
pages = {152-163},
timestamp = {2021-04-16T02:31:49.000+0200},
title = {Fast multipole boundary element method for the Laplace equation in a locally perturbed half-plane with a Robin boundary condition},
url = {https://www.sciencedirect.com/science/article/pii/S0045782512001326},
volume = {233-236},
year = 2012
}