Topology Finite Element Method For Electromagnetic Field Problems

As a numerical method, the finite element method (FEM) has very important status in electromagnetic field problems for it has the virtues of sparse and symmetrical coefficient matrix, can fitting the boundary closely, easy to disposal boundary conditions, which is a powerful tool to compute electromagnetic field problems.Generated grids to discrete field and FEM equation solution are two important sections in implement of FEM. Generate grids quickly and accurately to discrete the field is the precondition and bottleneck of FEM. How to improve the efficiency for coefficient matrix storage and solve the equation quickly is the hotspot of recent research. Both sections are discussed in this paper. In this paper, many usual triangulation methods are compared, also, this paper present a method combine Advanced Front Method (AFM) with Delaunay triangulation, which can be use in arbitrary field's triangulation. Base on the research of usual equation solution and the theory of topology finite element method (TFEM), a new algorithm combine TFEM with new preconditioning conjugate gradient method (PCGM) was presented. The new algorithm can take full advantages of TFEM, it can save the memories, reduce time spending in calculation and simplified the program, it has superiority when the amount of nodes is huge. In this paper, the new algorithm and triangulation are achieved with Visual C++, the validity of the new algorithm was proved by several example.