Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks
Article
Article Title | Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks |
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ERA Journal ID | 3475 |
Article Category | Article |
Authors | Mai-Duy, N. (Author) and Tran-Cong, T. (Author) |
Journal Title | Engineering Analysis with Boundary Elements |
Journal Citation | 30 (2), pp. 77-87 |
Number of Pages | 11 |
Year | 2006 |
Publisher | Elsevier |
Place of Publication | Oxford, United Kingdom |
ISSN | 0955-7997 |
1873-197X | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.enganabound.2005.10.004 |
Web Address (URL) | https://www.sciencedirect.com/science/article/abs/pii/S0955799705002018 |
Abstract | This paper reports a new indirect radial-basis-function (RBF) collocation method for numerically solving biharmonic boundary-value problems. The RBF approximations are constructed through an integration process. The new feature here is that integration constants are eliminated pointwise using the prescribed boundary conditions rather than employed as network weights. This treatment of integration constants is particularly well suited for the case of discretizing the governing differential equations on a set of scattered points. The proposed method is verified through the solution of benchmark test problems. Accurate results and high convergence rates are obtained. |
Keywords | indirect radial-basis-function networks; point collocation; meshless method; biharmonic equations; multiple boundary conditions |
ANZSRC Field of Research 2020 | 490199. Applied mathematics not elsewhere classified |
490406. Lie groups, harmonic and Fourier analysis | |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | University of Sydney |
Department of Mechanical and Mechatronic Engineering |
https://research.usq.edu.au/item/9y0vx/solving-biharmonic-problems-with-scattered-point-discretization-using-indirect-radial-basis-function-networks
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