Application Of Transfinite Elements Method In The Simulation Of Microwave Passive Component

With the rapid development of computer technology, the finite element method developed rapidly that with high accuracy and computationally intensive. Today the finite element method has become the mainstream method of electromagnetic problems analysis and calculation. Due to the finite element has a wealth of basis function, it can be used to solve complex structure and inhomogeneous media electromagnetic problems. The research of the finite element method is also increasing. Meanwhile, application of the finite element method in the infinite domain problem has made great progress. FEM grid through appropriate truncation get virtual boundaries to achieve truncated infinite space, and it is used to deal with real problems and achieved the desired results. There have several more classic approach infinite domain boundary truncated, for example, PML matching layer, boundary integral method, etc. Each method has advantages and disadvantages. So it is necessary to study truncation boundary deal with the problem. Focus of this paper is through the vector finite element method and transfinite element to deal with regular.The main content of this paper:First of all, this paper is to discuss the basic principles of the finite element method and the basic steps to achieve the finite element method. This paper describes the basis functions and edge-numbering scheme, as well as synthetic matrix. And then using vector finite element method for the rectangular cavity eigenvalue problem is analyzed, get the finite element matrix and calculate the final result. It clears the specific implementation method of the finite element methodOn the basis of vector finite element, the paper followed by a weak statement of Helmholtz equation obtained by the Galerkin method. Then, this paper uses the method of numerical integration and the weak statement for Helmholtz equation to processing the regular waveguide truncation. The GSS package is used to calculate the results.The software VisIt through the final calculated result, draw electric cloud and the electric field vector. This paper based on the weak statement for the Helmholtz equation in conjunction with the Galerkin method to study the transfinite element method.Through a series of calculations to derive the matrix equation and then used in calculation.This method ensures the sparse characteristic of finite element matrix. Meanwhile, the final finite element matrix is composed of general finite element matrix data and truncated boundary calculated result, logic is clear, more likely to synthesize the final matrix. Compare with the numerical integration method, the matrix of transfinite element method required storage space is greatly reduced.Finally, the paper summarizes the main work of this paper, according to the research process and the problems presented follow-up content.