In this paper, a meshless method based on the generalized finite difference method is proposed for the 2D and 3D anisotropic elliptic interface problem. The method is convenient to deal with the mixed derivatives brought by the anisotropy, as well as the 2D and 3D complex geometries of the interfaces. Moreover, the treatment of different interfaces only needs to change their level set functions. Several 2D and 3D numerical experiments are provided and compared with the finite element-finite difference method to illustrate the features of the proposed method.

中文翻译：

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基于广义有限差分法的2D和3D各向异性椭圆界面问题的无网格方法

本文针对2D和3D各向异性椭圆界面问题提出了一种基于广义有限差分法的无网格方法。该方法可以方便地处理各向异性带来的混合导数以及界面的2D和3D复杂几何形状。而且，不同接口的处理只需要改变它们的水平集函数即可。提供了几个 2D 和 3D 数值实验，并与有限元-有限差分法进行比较，以说明该方法的特点。