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Subdomain radial basis collocation method for heterogeneous media
Author(s) -
Chen JiunShyan,
Wang Lihua,
Hu HsinYun,
Chi ShengWei
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2624
Subject(s) - collocation (remote sensing) , collocation method , convergence (economics) , interface (matter) , basis (linear algebra) , mathematics , radial basis function , boundary (topology) , orthogonal collocation , boundary value problem , dirichlet boundary condition , smoothness , partial differential equation , exponential function , basis function , mathematical optimization , computer science , mathematical analysis , differential equation , geometry , ordinary differential equation , bubble , machine learning , maximum bubble pressure method , parallel computing , economic growth , artificial neural network , economics
Strong form collocation in conjunction with radial basis approximation functions offer implementation simplicity and exponential convergence in solving partial differential equations. However, the smoothness and nonlocality of radial basis functions pose considerable difficulties in solving problems with local features and heterogeneity. In this work, we propose a simple subdomain strong form collocation method, in which the approximation in each subdomain is constructed separately. Proper interface conditions are then imposed on the interface. Under the subdomain strong form collocation construction, it is shown that both Neumann and Dirichlet boundary conditions should be imposed on the interface to achieve the optimum convergence. Error analysis and numerical tests consistently confirm the need to impose the optimal interface conditions. The performance of the proposed methods in dealing with heterogeneous media is also validated. Copyright © 2009 John Wiley & Sons, Ltd.