Kansa method for problems with weak discontinuity / Artur Krowiak, Renata Filipowska // W: International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018), Rhodes, Greece, 13-18 September ... więcej

Kansa method for problems with weak discontinuity / Artur Krowiak, Renata Filipowska // W: International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018), Rhodes, Greece, 13-18 September 2018 [Dokument elektroniczny] / eds. Theodore Simos, Charalambos Tsitouras. – [Melville] : AIP Publishing, 2019. – (AIP Conference Proceedings, ISSN 1551-7616 ; 2116). – S. [1-4] : wykr. – Tryb dostępu: https://aip.scitation.org/doi/pdf/10.1063/1.5114488?class=pdf. – Oznaczenie ref./art.: 450021. – Bibliogr. 8 poz., Abstr. – doi: 10.1063/1.5114488. – ISBN 978-0-7354-1854-7

The paper deals with the use of a global radial basis function collocation method (Kansa method) to problems described by differential equations with non-continuous coefficients. The derivative of the ... więcej

The paper deals with the use of a global radial basis function collocation method (Kansa method) to problems described by differential equations with non-continuous coefficients. The derivative of the solution in such problems can possess a jump, which is difficult to capture by global methods. Therefore, to take advantage of the power of this technique, reflecting in very high order of convergence, in the paper, some modifications that allow to apply the method to such problems are introduced. One of these modifications divides the solution domain into subdomains, in which the coefficients are continuous and uses appropriate continuity conditions on the interface, the other one introduces additional degrees of freedom into the interpolant and uses additional interface conditions to increase accuracy of the solution. The approaches are examined by one-dimensional benchmark problems.