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Volume 26, Issue 2
The Finite Point Method for Solving the 2-D 3-T Diffusion Equations

Guixia Lv & Longjun Shen

DOI: 10.4208/cicp.OA-2017-0223

Commun. Comput. Phys., 26 (2019), pp. 413-433.

Published online: 2019-04

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  • Abstract

A new approach for numerically solving 3-T diffusion equations on 2-D scattered point distributions is developed by the finite point method. In this paper, a new method for selecting neighboring points is designed, which is robust and well reflects variations of gradients of physical quantities. Based on this, a new discretization method is proposed for the diffusion operator, which results in a new scheme with the stencil of minimal size for numerically solving nonlinear diffusion equations. Distinguished from most of meshless methods often involving dozens of neighboring points, this method needs only five neighbors of the point under consideration. Numerical simulations show the good performance of the proposed methodology.

  • Keywords

Finite point method, 2-D 3-T diffusion equations, minimal stencil, method for selecting neighboring points.

  • AMS Subject Headings

65D25, 65M06, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-413, author = {Guixia Lv and Longjun Shen}, title = {The Finite Point Method for Solving the 2-D 3-T Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {413--433}, abstract = {

A new approach for numerically solving 3-T diffusion equations on 2-D scattered point distributions is developed by the finite point method. In this paper, a new method for selecting neighboring points is designed, which is robust and well reflects variations of gradients of physical quantities. Based on this, a new discretization method is proposed for the diffusion operator, which results in a new scheme with the stencil of minimal size for numerically solving nonlinear diffusion equations. Distinguished from most of meshless methods often involving dozens of neighboring points, this method needs only five neighbors of the point under consideration. Numerical simulations show the good performance of the proposed methodology.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0223}, url = {http://global-sci.org/intro/article_detail/cicp/13097.html} }
TY - JOUR T1 - The Finite Point Method for Solving the 2-D 3-T Diffusion Equations AU - Guixia Lv & Longjun Shen JO - Communications in Computational Physics VL - 2 SP - 413 EP - 433 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2017-0223 UR - https://global-sci.org/intro/article_detail/cicp/13097.html KW - Finite point method, 2-D 3-T diffusion equations, minimal stencil, method for selecting neighboring points. AB -

A new approach for numerically solving 3-T diffusion equations on 2-D scattered point distributions is developed by the finite point method. In this paper, a new method for selecting neighboring points is designed, which is robust and well reflects variations of gradients of physical quantities. Based on this, a new discretization method is proposed for the diffusion operator, which results in a new scheme with the stencil of minimal size for numerically solving nonlinear diffusion equations. Distinguished from most of meshless methods often involving dozens of neighboring points, this method needs only five neighbors of the point under consideration. Numerical simulations show the good performance of the proposed methodology.

Guixia Lv and Longjun Shen. (2019). The Finite Point Method for Solving the 2-D 3-T Diffusion Equations. Communications in Computational Physics. 26 (2). 413-433. doi:10.4208/cicp.OA-2017-0223
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