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Applications of RBF collocation method to elliptic PDEs in an arbitrary domain by fictitious domain extensions
Author(s) -
Chen JiahnHorng
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700879
Subject(s) - domain (mathematical analysis) , collocation (remote sensing) , fictitious domain method , collocation method , mathematics , boundary (topology) , radial basis function , mathematical analysis , elliptic curve , extension (predicate logic) , function (biology) , boundary value problem , simple (philosophy) , computer science , differential equation , artificial intelligence , artificial neural network , ordinary differential equation , philosophy , epistemology , machine learning , evolutionary biology , biology , programming language
A fictitious domain extension approach is introduced to study elliptic PDE's defined in arbitrary domains by the radial basis function (RBF) collocation method. In this approach, arbitrary physical geometries are extended to domains which are topologically rectangular. The solution domain is also extended to the fictitious area and assumed to satisfy the same governing equation in it and on its extended boundaries. The boundary conditions are still specified on the boundaries of the original physical domain. The problem in the extended domain becomes ill‐posed. However, it can be easily circumvented by the collocation method. We demonstrate that the solution can be directly obtained without domain decompositions and iterations. The new approach is simple, efficient and accurate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)