Moving least square: one dimensional integrated radial basis function networks for time dependent problems
Paper
Paper/Presentation Title | Moving least square: one dimensional integrated radial basis function networks for time dependent problems |
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Presentation Type | Paper |
Authors | Ngo-Cong, D. (Author), Mai-Duy, N. (Author), Karunasena, W. (Author) and Tran-Cong, T. (Author) |
Editors | Brebbia, C. A. and Popov, V. |
Journal or Proceedings Title | Boundary Elements and other Mesh Reduction Methods XXXIII |
Journal Citation | 52, pp. 309-320 |
Number of Pages | 12 |
Year | 2011 |
Place of Publication | Southampton, UK |
ISBN | 9781845645427 |
Digital Object Identifier (DOI) | https://doi.org/10.2495/BE110271 |
Web Address (URL) of Paper | http://library.witpress.com/pages/PaperInfo.asp?PaperID=22406 |
Conference/Event | 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011) |
Event Details | 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011) Event Date 28 to end of 30 Jun 2011 Event Location New Forest, United Kingdom |
Abstract | This paper presents a new numerical procedure for time-dependent problems. The partition of unity method is employed to incorporate the moving least square and one-dimensional integrated radial basis function networks techniques in an approach (MLS-1D-IRBFN) that produces a very sparse system matrix and offers as a high order of accuracy as that of global 1D-IRBFN method. Moreover, the proposed approach possesses the Kronecker-$\delta$ property which helps impose the essential boundary condition in an exact manner. Spatial derivatives are discretised using Cartesian grids and MLS-1D-IRBFN, whereas temporal derivatives are discretised using high-order time-stepping schemes, namely standard $\theta$ and fourth-order Runge-Kutta methods. Several numerical examples including two-dimensional diffusion equation, one-dimensional advection-diffusion equation and forced vibration of a beam are considered. Numerical results show that the current methods are highly accurate and efficient in comparison with other published results available in the literature. |
Keywords | time-dependent problems, integrated radial basis functions, moving least square, partition of unity, Cartesian grids |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Centre of Excellence in Engineered Fibre Composites | |
Institution of Origin | University of Southern Queensland |
Book Title | Boundary Elements and Other Mesh Reduction Methods XXXIII |
https://research.usq.edu.au/item/q1227/moving-least-square-one-dimensional-integrated-radial-basis-function-networks-for-time-dependent-problems
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