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Boundary element method for spatially‐periodic potential problems
Author(s) -
Ogata Hidenori
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700017
Subject(s) - boundary element method , discretization , method of fundamental solutions , singular boundary method , neumann boundary condition , mathematics , boundary knot method , mathematical analysis , laplace transform , mixed boundary condition , dirichlet boundary condition , boundary value problem , boundary (topology) , laplace's equation , operator (biology) , dirichlet distribution , integral equation , element (criminal law) , finite element method , engineering , structural engineering , biochemistry , chemistry , repressor , transcription factor , gene , law , political science
In this paper, we propose a boundary element method for two‐dimensional potential problems with one‐dimensional spatial periodicity, which have been difficult to be solved by the ordinary boundary element method. In the presented method, we reduce the potential problems with Dirichlet and Neumann boundary conditions to integral equation problems with the periodic fundamental solution of the Laplace operator and, then, obtain approximate solutions by solving linear systems given by discretizing the integral equations. Numerical examples are also included. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)