Premium
Comparing RBF‐FD approximations based on stabilized Gaussians and on polyharmonic splines with polynomials
Author(s) -
Santos L. G. C.,
ManzanaresFilho N.,
Me G. J.,
Abreu E.
Publication year - 2018
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.5813
Subject(s) - radial basis function , mathematics , domain (mathematical analysis) , boundary (topology) , poisson's equation , function (biology) , mathematical analysis , computer science , artificial intelligence , artificial neural network , evolutionary biology , biology
Summary In this work, we are concerned with radial basis function–generated finite difference (RBF‐FD) approximations. Numerical error estimates are presented for stabilized flat Gaussians (RBF(SGA)‐FD) and polyharmonic splines with supplementary polynomials (RBF(PHS)‐FD) using some analytical solutions of the Poisson equation in a square domain. Both structured and unstructured point clouds are employed for evaluating the influence of cloud refinement, size of local supports, and maximal permissible degree of the polynomials in RBF(PHS)‐FD. High order of accuracy was attained with both RBF(SGA)‐FD and RBF(PHS)‐FD especially for unstructured clouds. Absolute errors in the first and second derivatives were also estimated at all points of the domain using one of the analytical solutions. For RBF(SGA)‐FD, this test showed the occurrence of improprieties of some decentered supports localized on boundary neighborhoods. This phenomenon was not observed with RBF(PHS)‐FD.