Hybrid Approach of Radial Basis Function and Domain Decomposition Method based on FEM with Different Shape of sub-domains for Electromagnetic Problems

摘要

A novel approach, radial basis function (RBF) mixed with domain decomposition method (DDM) based on Galerkin finite element method (FEM) has been introduced in our previous work. The proposed method divides the computational domain into a series of rectangular sub-domains, and each sub-domain is taken as a separate calculation area to get the solution expression and shape function by using the point interpolation based on RBF. Then, sub-domains are taken as elements of the Galerkin FEM to approximate the entire solutions. The hybrid approach has been proved as a valid method, and inherited advantages of RBF and FEM. Nevertheless, the shape of sub-domain needs to be rectangular in that work and there are many different shapes in practical problems. More flexible form can be better adapted to electromagnetic problems. Triangular and cubical sub-domains will be investigated, respectively. In order to verify the improved method, several numerical examples including 3-D electromagnetic problem will be computed.