Based On Triangular Prism Grid Three-dimensional Vector Finite Element Method

Numerical techniques have become a major force in the field of applied electromagnetic. One of the important techniques used is the Finite Element Method (FEM). It is very popular in mechanical and civil engineering because it allows the analysis of complex structures. It also is computationally efficient because it yields sparse matrices.In this paper, the triangular prism elements are used for discretizing the computational domain with Edge-Based Vector Finite Element Method. To date, the tetrahedron is often the element for discretizing the computational domain. In fact, the triangular prism element is another choice in numerical solutions of electromagnetic field problems. This kind of element is very suitable for the discretization of multilayered structures and deep cavities, which are unstructured in two dimensions and structured in the third dimension. We perform discretization in the way that the triangular prism elements extrude along the layer-growth direction while capturing the irregular geometry in the transverse cross section.The Edge-Based Vector Finite Element Method using the triangular prism as the element for discretization is proposed in this paper. At the very beginning, the basic theory of FEM is studied. The basic analytical routine for the Edge-Based Vector FEM using any of the elements is same, which is on the basis of conventional FEM. However, how to perform the analysis of the FEM concretely is of great difference when different elements are used for discretization. That is to say, what we do is to study the concrete way to perform the analysis of FEM step by step. And the most important task is the derivation of the vector basis functions for the triangular prism element and the generation of the matrix system.A platform for numerical simulation is built based on the algorithm what we present, including the preprocessing routines, the matrix generation and the post-processing routines. Then we examine the validity of the presented edge-based functions by considering the eigenvalues of two different cavities using the triangular prism as the tessellation element, and discuss the performance of the algorithm and the platform.