Abstract

A point interpolation which bases on the radial function is a new meshless method. It is advantageous over the original
PIM with polynomial basis in avoiding singularity when shape functions are constructed. It is also easy to deal with
essential boundary for its property of Kronecher Delta function. To verify it’s valid, this paper introduced the basic
principle of RPIM. In addition, numerical example of heat conduction showed that the new methods possessed several
advantages, such as high eciency, high accuracy, and high stability. It is a promising method in physics.

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