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首页> 外文期刊>Engineering analysis with boundary elements >Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion-convection equations
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Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion-convection equations

机译：使用径向基函数的笛卡尔网格方法用于求解Poisson，Helmholtz和扩散对流方程

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摘要

Four methods that solve the Poisson, Helmholtz, and diffusion-convection problems on Cartesian grid by collocation with radial basis functions are presented. Each problem is split into a problem with an inhomogeneous equation and homogeneous boundary conditions, and a problem with a homogeneous equation and inhomogeneous boundary conditions. The former problem is solved by collocation with multiquadrics, whereas the latter problem is solved by collocation with either multiquadrics or fundamental solutions. It is found that methods that make use of fundamental solutions for collocation yield more accurate solutions that are less sensitive to the shape parameter of multiquadrics and node arrangement. Additional collocation appears to improve the quality of solutions. (C) 2004 Elsevier Ltd. All fights reserved.
机译：提出了通过与径向基函数并置来解决笛卡尔网格上的泊松，亥姆霍兹和扩散对流问题的四种方法。每个问题都分解为一个具有不均匀方程和齐次边界条件的问题，以及一个具有齐次方程和不齐次边界条件的问题。前一个问题通过与多二次元搭配解决，而后一个问题通过与多二次元搭配基本解决方案解决。发现使用基本解进行搭配的方法会产生更精确的解，对多二次方的形状参数和节点排列不太敏感。附加配置似乎可以提高解决方案的质量。 （C）2004 Elsevier Ltd.版权所有。

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