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A multidomain integrated‐radial‐basis‐function collocation method for elliptic problems
Author(s) -
MaiDuy N.,
TranCong T.
Publication year - 2008
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.20319
Subject(s) - radial basis function , mathematics , discretization , collocation (remote sensing) , partial derivative , domain (mathematical analysis) , partial differential equation , collocation method , orthogonal collocation , function (biology) , elliptic partial differential equation , basis function , basis (linear algebra) , mathematical analysis , differential equation , ordinary differential equation , computer science , geometry , artificial neural network , machine learning , evolutionary biology , biology
This article is concerned with the use of integrated radial‐basis‐function networks (IRBFNs) and nonoverlapping domain decompositions (DDs) for numerically solving one‐ and two‐dimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means of one‐dimensional IRBFNs. A distinguishing feature of the present DD technique is that the continuity of the RBF solution across the interfaces is enforced with one order higher than with conventional DD techniques. Several test problems governed by second‐ and fourth‐order differential equations are considered to investigate the accuracy of the proposed technique. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008