New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils
Article
Article Title | New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils |
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ERA Journal ID | 3475 |
Article Category | Article |
Authors | Mai-Duy, Nam (Author) and Strunin, Dmitry (Author) |
Journal Title | Engineering Analysis with Boundary Elements |
Journal Citation | 125, pp. 12-22 |
Number of Pages | 11 |
Year | 2021 |
Publisher | Elsevier |
Place of Publication | United Kingdom |
ISSN | 0955-7997 |
1873-197X | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.enganabound.2021.01.001 |
Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0955799721000011 |
Abstract | This paper presents some new compact approximation stencils based on integrated radial basis functions (IRBFs) for numerically solving second-order elliptic differential problems on Cartesian grids. Higher-order IRBF schemes are employed to approximate the field/dependent variable. The IRBF approximations in each direction are based on 3 points and constructed independently, where derivatives of the second, third, fourth, fifth and sixth orders along the grid line are enforced at the two end-points. The imposed nodal derivative values are simply acquired through a Picard-type iteration scheme. The stencil is made up of 3 points and 5 points for 1D and 2D discretisations, respectively. Numerical results show that the proposed stencils yield a high rate of convergence with respect to grid refinement, e.g. up to the 13th order for 1D problems and to the 9th order for 2D problems. |
Keywords | Compact approximation; Local approximation; Integrated radial basis function; 3-point stencil; 5-point stencil |
ANZSRC Field of Research 2020 | 401706. Numerical modelling and mechanical characterisation |
490303. Numerical solution of differential and integral equations | |
Byline Affiliations | School of Mechanical and Electrical Engineering |
School of Sciences | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q6w0v/new-approximations-for-one-dimensional-3-point-and-two-dimensional-5-point-compact-integrated-rbf-stencils
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