Meshless numerical method based on tensor product

Abstract

A normalized space constructed by tensor product is used in field function approach to give a special case of moving least squares (MLS) interpolation scheme. In the regular domain, the field function which meets homogenous boundary conditions is constructed by spanning base space to make the MLS interpolation scheme simpler and more efficient. Owing to expanded basis functions selection, some drawbacks in general MLS method, for example repeated inversion, low calculation efficiency, and complex criterions, can be avoided completely. Numerical examples illustrate that the proposed method is characterized by simple mathematical concept, convenient repeat calculations with high accuracy, good continuity, less computation and rapid convergence.

Keywords

weighted function / tensor product / normalized space / general variational principle