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Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel

Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel AbstractThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel

Curved and Layered Structures , Volume 7 (1): 12 – Jan 1, 2020

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References (26)

Publisher
de Gruyter
Copyright
© 2020 Artur Krowiak, published by De Gruyter
eISSN
2353-7396
DOI
10.1515/cls-2020-0006
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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.

Journal

Curved and Layered Structuresde Gruyter

Published: Jan 1, 2020

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