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Volume 13, Issue 3
A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains

Xin Lu, Ping Zhang, Liwei Shi, Songming Hou & Ying Kuang

Adv. Appl. Math. Mech., 13 (2021), pp. 645-670.

Published online: 2020-12

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  • Abstract

In this paper, we use the radial basis function meshless method to solve the irregular region interface problem. The key idea is to construct radial basis functions corresponding to different regions divided by the interfaces. This method avoids the difficulty of mesh generation, and is efficient in the numerical simulation of partial differential equations in irregular domain with variable matrix coefficients. The numerical error is effectively reduced by using the direct method to handle the interface jump conditions. Numerical simulation results show that the radial basis function meshless numerical method can effectively deal with various kinds of interface problems with irregular domains and sharp-edged interfaces, including Poisson equations, heat conduction equations and wave equations.

  • Keywords

Interface problem, irregular domain, matrix coefficient, partial differential equation, meshless method.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-645, author = {Lu , XinZhang , PingShi , LiweiHou , Songming and Kuang , Ying}, title = {A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {3}, pages = {645--670}, abstract = {

In this paper, we use the radial basis function meshless method to solve the irregular region interface problem. The key idea is to construct radial basis functions corresponding to different regions divided by the interfaces. This method avoids the difficulty of mesh generation, and is efficient in the numerical simulation of partial differential equations in irregular domain with variable matrix coefficients. The numerical error is effectively reduced by using the direct method to handle the interface jump conditions. Numerical simulation results show that the radial basis function meshless numerical method can effectively deal with various kinds of interface problems with irregular domains and sharp-edged interfaces, including Poisson equations, heat conduction equations and wave equations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0004}, url = {http://global-sci.org/intro/article_detail/aamm/18501.html} }
TY - JOUR T1 - A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains AU - Lu , Xin AU - Zhang , Ping AU - Shi , Liwei AU - Hou , Songming AU - Kuang , Ying JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 645 EP - 670 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0004 UR - https://global-sci.org/intro/article_detail/aamm/18501.html KW - Interface problem, irregular domain, matrix coefficient, partial differential equation, meshless method. AB -

In this paper, we use the radial basis function meshless method to solve the irregular region interface problem. The key idea is to construct radial basis functions corresponding to different regions divided by the interfaces. This method avoids the difficulty of mesh generation, and is efficient in the numerical simulation of partial differential equations in irregular domain with variable matrix coefficients. The numerical error is effectively reduced by using the direct method to handle the interface jump conditions. Numerical simulation results show that the radial basis function meshless numerical method can effectively deal with various kinds of interface problems with irregular domains and sharp-edged interfaces, including Poisson equations, heat conduction equations and wave equations.

Xin Lu, Ping Zhang, Liwei Shi, Songming Hou & Ying Kuang. (1970). A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains. Advances in Applied Mathematics and Mechanics. 13 (3). 645-670. doi:10.4208/aamm.OA-2020-0004
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