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The method of approximate particular solutions for solving anisotropic elliptic problems

机译:各向异性椭圆问题的近似特殊解法

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摘要

In this paper, we study the method of approximate particular solutions for solving anisotropic elliptic-type problems. A special norm associated with the anisotropic differential operator is introduced for the design of anisotropic radial basis functions. Particular solutions of anisotropic radial basis function can be found by the same procedure as that of regular radial basis functions under Laplace operator. Consequently, the method of approximate particular solutions can be extended to anisotropic elliptic-type problems. Numerical results are presented for a number of two-dimensional anisotropic diffusion problems. It shows that this method permits the choice of collocation points independent of the magnitude of anisotropy.
机译:在本文中,我们研究解决各向异性椭圆型问题的近似特定解的方法。为各向异性径向基函数的设计引入了与各向异性微分算子相关的特殊范数。各向异性径向基函数的特殊解可以通过与在Laplace算子下常规径向基函数相同的过程找到。因此,近似特定解的方法可以扩展到各向异性椭圆型问题。给出了许多二维各向异性扩散问题的数值结果。结果表明,该方法可以选择与各向异性大小无关的搭配点。

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