Comparing RBF-FD approximations based on stabilized Gaussians and on polyharmonic splines with polynomials

Autor(es)

Santos, L. G. C. ^[1] ; Manzanares-Filho, N. ^[1] ; Menon, G. J. ^[1] ; Abreu, E. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Itajuba, Inst Mech Engn, 1303 BPS Ave, Itajuba, MG - Brazil

^[2] Univ Estadual Campinas, Inst Math Stat & Comp Sci, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 115, n. 4, p. 462-500, JUL 27 2018.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 16/23374-1 - Leis de conservação, leis de equilíbrio e EDPs relacionadas com fluxos descontínuos e não-locais em ciências aplicadas: análise numérica, teoria e aplicações
• Beneficiário: Eduardo Cardoso de Abreu
• Modalidade de apoio: Auxílio à Pesquisa - Regular