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

作者：Perez Arancibia Carlos^*; Ramaciotti Pedro; Hein Ricardo; Duran Mario

来源：Computer Methods in Applied Mechanics and Engineering, 2012, 233: 152-163.

DOI：10.1016/j.cma.2012.04.012

• Laplace equation
• Robin boundary condition
• Fast multipole algorithm
• Boundary element method
• Exponential integral function

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%26apos;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.

• 出版日期2012-8