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Domain decomposition for radial basis meshless methods
Author(s) -
Li Jichun,
Hon Y. C.
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10096
Subject(s) - radial basis function , grid , domain decomposition methods , domain (mathematical analysis) , mathematics , meshfree methods , matching (statistics) , algorithm , basis function , block (permutation group theory) , finite element method , function (biology) , regularized meshless method , mathematical optimization , partial differential equation , decomposition , basis (linear algebra) , computer science , mathematical analysis , geometry , singular boundary method , artificial intelligence , boundary element method , ecology , statistics , physics , evolutionary biology , biology , artificial neural network , thermodynamics
Both overlapping and nonoverlapping domain decomposition methods (DDM) on matching and nonmatching grid have been developed to couple with the meshless radial basis function (RBF) method. Example shows that overlapping DDM with RBF can achieve much better accuracy with less nodal points compared to FDM and FEM. Numerical results also show that nonmatching grid DDM can achieve almost the same accuracy within almost the same iteration steps as the matching grid case; hence our method is very attractive, because it is much easier to generate nonmatching grid just by putting blocks of grids together (for both overlapping and nonoverlapping), where each block grid can be generated independently. Also our methods are showed to be able to handle discontinuous coefficient. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 450–462, 2004.