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Radial Basis Function methods—reduced computational expense by exploiting symmetry
Author(s) -
Sarra Scott A.
Publication year - 2018
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.22272
Subject(s) - radial basis function , mathematics , interpolation (computer graphics) , algorithm , basis function , matrix (chemical analysis) , simple (philosophy) , function (biology) , linear algebra , basis (linear algebra) , domain decomposition methods , domain (mathematical analysis) , mathematical optimization , symmetry (geometry) , finite element method , computer science , mathematical analysis , geometry , artificial intelligence , image (mathematics) , artificial neural network , philosophy , materials science , physics , epistemology , composite material , evolutionary biology , biology , thermodynamics
Radial basis function (RBF) methods are popular methods for scattered data interpolation and for solving PDEs in complexly shaped domains. RBF methods are simple to implement as they only require elementary linear algebra operations. In this work, center locations that result in matrices with a centrosymmetric structure are examined. The resulting matrix structure can be exploited to reduce computational expense and improve the accuracy of the methods while avoiding more complicated techniques such as domain decomposition.