Application of a kernel method with stably evaluated Gaussian kernel to problems on irregular domains / Artur Krowiak, Renata Filipowska // W: International Conference of Computational Methods in Sciences ... więcej

Application of a kernel method with stably evaluated Gaussian kernel to problems on irregular domains / Artur Krowiak, Renata Filipowska // W: International Conference of Computational Methods in Sciences and Engineering ICCMSE 2020 [Dokument elektroniczny] / eds. Theodore Simos, Zacharoula Kalogiratou, Theodore Monovasilis. – Melville : AIP Publishing, 2021. – (AIP Conference Proceedings, ISSN 1551-7616 ; 2343). – 4 s. : rys., tab. – Tryb dostępu: https://aip.scitation.org/doi/abs/10.1063/5.0047781. – Oznaczenie ref./art.: 130004. – Bibliogr. 7 poz., Abstr. – Mat. konf.: ICCMSE-2020, Crete, Greece, 29.04-03.05.2020. – doi: 10.1063/5.0047781. – ISBN 978-0-7354-4088-3

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 ... więcej

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.