Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel
Authors:
- Artur Krowiak
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 biharmonic problems on quadrilateral irregular domains. As an example, in the present work this approach is applied to solve bending as well as free vibration problem of thin plates. In the paper some strategies for the implementation of the boundary conditions are also presented and examined due to the accuracy. The numerical tests show high accuracy and usefulness of the method.
- Record ID
- CUT977849ab29ea4e71bc39f1ec3e6c597e
- Publication categories
- ;
- Author
- Journal series
- Curved and Layered Structures, ISSN 2353-7396
- Issue year
- 2020
- Vol
- 7
- No
- 20
- Pages
- 56-67
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 66-67; Bibliografia (liczba pozycji) - 25; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 7, Iss. 20
- Keywords in English
- stable RBF basis, Mercer series, Gaussian kernel, blending functions, biharmonic equation
- DOI
- DOI:10.1515/cls-2020-0006 Opening in a new tab
- URL
- https://www.degruyter.com/view/journals/cls/7/1/article-p56.xml Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT977849ab29ea4e71bc39f1ec3e6c597e/
- URN
urn:pkr-prod:CUT977849ab29ea4e71bc39f1ec3e6c597e
* 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.