Computing high-order derivatives in compact integrated-RBF stencils
Article
Article Title | Computing high-order derivatives in compact integrated-RBF stencils |
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ERA Journal ID | 3475 |
Article Category | Article |
Authors | Mai-Duy, N. (Author), Strunin, D. (Author) and Karunasena, W. (Author) |
Journal Title | Engineering Analysis with Boundary Elements |
Journal Citation | 135, pp. 369-381 |
Number of Pages | 13 |
Year | 2022 |
Publisher | Elsevier |
Place of Publication | United Kingdom |
ISSN | 0955-7997 |
1873-197X | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.enganabound.2021.11.025 |
Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0955799721003507 |
Abstract | In Mai-Duy and Strunin (Mai-Duy and Strunin, 2021), it was shown that the inclusion of nodal values of high-order derivatives in compact local integrated-radial-basis-function (IRBF) stencils results in a significant improvement in the solution accuracy. The purpose of this work is to examine in detail the numerical performance of several approximation schemes based on one-dimensional IRBFs for computing high-order derivatives along the grid lines. The extended precision floating point arithmetic is utilised to achieve a high level of accuracy, and the efficiencies of the approximation schemes are improved by employing overlapping domain decomposition and mixed-precision calculations. In solving partial differential equations (PDEs), the proposed 1D-IRBFs are implemented using the RBF widths that are fixed and vary with grid refinement. A simple framework is presented to cover the two RBF width cases, and a numerical analysis is carried out for differential problems with slow and rapid variations in their solutions. In solving the convection–diffusion equations, the proposed 1D-IRBFs are also incorporated into the upwind schemes for effectively simulating highly-nonlinear flows. Numerical results show that high rates of convergence with respect to grid refinement are achieved with both fixed and variable widths. |
Keywords | High-order derivatives; High-order upwind schemes; Compact approximations; Integrated radial basis functions; Two-dimensional 5-point stencils; RBF widths |
ANZSRC Field of Research 2020 | 401706. Numerical modelling and mechanical characterisation |
490399. Numerical and computational mathematics not elsewhere classified | |
Byline Affiliations | School of Mechanical and Electrical Engineering |
School of Sciences | |
School of Civil Engineering and Surveying | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q6z3z/computing-high-order-derivatives-in-compact-integrated-rbf-stencils
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