The fundamental solution element method based on irregular polygonal meshes

In this paper, a novel implementation of the virtual element method is proposed, which employs fundamental solutions (Green functions) instead of polynomials. Instead of constructing explicit shape functions for polygonal elements, abstract basis functions are employed, which are only computable on the boundaries of elements. With the help of the projection into the space of fundamental solutions, the incomputable domain integration is eliminated. In addition, the source points of the fundamental solutions are moved outside the elements to ensure the boundness of the basis functions. Compared with the conventional implementation which projects into the space of polynomials, the numerical results demonstrate that the proposed method exhibits significant superiority in singular problems or when the number of nodes in elements is large.