Application of a kernel method with stably evaluated Gaussian kernel to problems on irregular domains
Authors:
- Artur Krowiak,
- Renata Filipowska
Abstract
The paper extends recently developed idea of stable evaluation of the Gaussian kernel. Owing to this, the Gaussian radial basis function that is sensitive to the shape parameter can be stably evaluated and applied to interpolation problems as well as to solve differential equations, giving highly accurate results. But it can be done only with grids being the Cartesian product of sets of points, what limits the use of this idea to rectangular domains. In the present paper, by the association of an appropriate transformation with the mentioned method, the latter is applied to solve differential equations on quadrilateral irregular domains. As an example a biharmonic problem is taken into consideration. The numerical tests show high accuracy and usefulness of the method.
- Record ID
- CUT3b44e3c74a3049d3ac471bf96dfafb59
- Publication categories
- ; ;
- Author
- Pages
- [1-4]
- Other elements of collation
- rys.; tab.; Bibliografia (na s.) - 4; Bibliografia (liczba pozycji) - 7; Oznaczenie streszczenia - Abstr.
- Book
- Simos Theodore, Theodore Simos Kalagiratou Zacharoula, Zacharoula Kalagiratou Monovasilis Theodore Theodore Monovasilis (eds.): International Conference of Computational Methods in Sciences and Engineering ICCMSE 2020, AIP Conference Proceedings, no. 2343, 2021, Melville, American Institute of Physics, AIP Publishing, 4 p., ISBN 978-0-7354-4088-3
- Keywords in English
- kernel method, meshless method, irregular domain
- DOI
- DOI:10.1063/5.0047781 Opening in a new tab
- URL
- https://aip.scitation.org/doi/abs/10.1063/5.0047781 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT3b44e3c74a3049d3ac471bf96dfafb59/
- URN
urn:pkr-prod:CUT3b44e3c74a3049d3ac471bf96dfafb59
* 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.