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Point collocation method based on the FMLSRK approximation for electromagnetic field analysis

This paper presents the methodology of a mesh-free point collocation method and its application to the electromagnetic field computation. The special emphasis in this paper is on a point collocation scheme based on the fast moving least square reproducing kernel(FMLSRK) method with a variable dilation function. The concept of dilation function is newly introduced here, and we combine it with the conventional FMLSRK method. They yield the FMLSRK approximation operators. In the point collocation method using such an extended FMLSRK method, there is no need to construct integration cells, and any type of boundary conditions can be directly enforced. Numerical simulations for a two-dimensional (2-D) electromagnetic field on complicated geometry are carried out to validate the reliability of proposed method, in which the dilation function plays an essential role.