Rapid Analysis Of Microwave Circuits With The Finite Element Method

This paper is focused on the rapid analysis of microwave circuits with finite element method in frequency-domain and time-domain. At first, the p-version multigrid method based on hierarchical high order basis functions is used in3D electromagnetic simulation with the frequency-domain finite-element method. In this method, the low frequency error components can be corrected on low order basis functions which are corresponding to the coarser grid. These low frequency error components can be used to calibrate and eliminate the alanogues in exact solutions while high order basis functions are used. Thus, without reducing the computational accuracy, the better calculated performance can be obtained comparing to the preconditioned Conjugate Gradient method.In order to avoid the iterative solution for a large scale FEM matrix equation, the Domain Decomposition Method of FEM (DDM-FEM) is studied for frequency-domain analysis. In this method, the microwave circuit is decomposed in several domains according to the actual electromagnetic structures. In every domain, the FEM matrix equation can be acquired and solved independently. For the less number of unknowns in each domain, the direct solution can be used to accelerate the solving of the FEM matrix equation. In DDM-FEM, the reasonable transmission conditions should be used in order to guarantee the continuity of the tangential electromagnetic field on discontinuous interfaces. So the solution vector in a domain will relate the electromagnetic field not only in local domain, but also on interfaces which is imposed from adjacent domains. After several iterations, when the influence comes from the adjacent domain can be ignored, the whole solution space is in electromagnetic balance. For the DDM-FEM, according to the mixed boundary conditions on discontinuous interface, the Galerkin test basis functions are revised in this work mainly. In this way, the iterative convergence performance can be promoted largely. At the same time, the disposal of nonconformal meshes on discontinuous interface is analyzed detailedly. And the using of the mixed high order and low order Hierarchical basis functions in DDM-FEM is acted accurately in this work as well.Compared with the frequency-domain finite element method, the time-domain finite element method is more rigorous for the request of the computational speed. In this work, the Spectral-Element Time-Domain method (SETD) which is based on high order orthogonal vector basis functions is researched detailedly. The electromagnetic space with complex structures is discreted by curved hexahedrons using ANSYS software. If a central difference scheme is employed for the time differential, the explicit SETD equations can be obtained finally.The stability condition of the SETD method is studied in this work. Extracting the eigenvalues in SETD equation and discarding those larger ones which are larger than the maximum input angular frequency of the microwave network, by doing so,the time stability of the SETD method is improved significantly. In SETD method, the mass matrix T is block-diagonal and the inversion of this mass matrix can be obtained inexpensively. So the eigenvalues of the SETD equation can be extracted easly while the Arnoldi iteration is used. This method is validated in the simulation of metal resonator structure.For the electromagnetic simulation of large scale, the parallel processing technologies on SETD method is studied in this work. The SETD matrix which is related to the subprocess can be acquired in each corresponding subprocess. And the technology of compressed vector data transfer is used in solving equations, which can accelerate the exchange of the information among all the subprocess. So the allocation of the computer resources can be optimized and the computing time is reduced.In addition, according to two kinds of mathematical analysis models for ferrite material, the corresponding solutions with SETD method are proposed in this work. And the fast electromagnetic simulation for ferrite circulators is performed accurately. At the same time, the analysis theories of active nonlinear microwave circuit by the use of SETD are studied in this work. Through the introduction of the concept of lumped current, and modeling the lumped elements together with those distributing circuits which are around them, and connecting them with field-circuit coupling equations, the high efficient SETD simulation for passive, active, linear, non-linear microwave circuit can be achieved correctly.