Kansa method for problems with weak discontinuity
Authors:
- Artur Krowiak,
- Renata Filipowska
Abstract
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.
- Record ID
- CUTfe4abaa875234f0caddcfd5332a23e2f
- Publication categories
- ; ;
- Author
- Pages
- [1-4]
- Other elements of collation
- wykr.; Bibliografia (na s.) - 4; Bibliografia (liczba pozycji) - 8; Oznaczenie streszczenia - Abstr.
- Book
- Simos Theodore, Theodore Simos Tsitouras Charalambos Charalambos Tsitouras (eds.): International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018), Rhodes, Greece, 13-18 September 2018, AIP Conference Proceedings, no. 2116, 2019, [Melville], American Institute of Physics, AIP Publishing, 4 p., ISBN 978-0-7354-1854-7
- Keywords in English
- kansa method, radial basis functions, weak discontinuity, interface problem
- DOI
- DOI:10.1063/1.5114488 Opening in a new tab
- URL
- https://aip.scitation.org/doi/pdf/10.1063/1.5114488 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTfe4abaa875234f0caddcfd5332a23e2f/
- URN
urn:pkr-prod:CUTfe4abaa875234f0caddcfd5332a23e2f
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.