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Fast Finite Element Analysis in Electromagnetics
Author: PingXueWei
Tutor: ChenRuShan
School: Nanjing University of Technology and Engineering
Course: Electromagnetic Field and Microwave Technology
Keywords: Finite element technique Krylov space iterative method Preconditioning technique Parallel Computing Level the base function ptype multigrid iteration method Schwarz methods
CLC: TM15
Type: PhD thesis
Year: 2007
Downloads: 626
Quote: 8
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Abstract
In many practical engineering areas, the application of numerical simulation methods can not only decrease the costs of productions and reduce the experimental period, but also guarantee the reliability of productions. As a result, numerical methods have become more and more important with the development of electrical computers and modern science and technologies. The superiority of an excellent numerical simulation method depends not only on the accuracy to simulate practical physical problems, but also on the efficiency of solving physical problems, i.e. the required memory and solution time should be as few as possible. For a given problem, the computational precision and the required CPU time, the required memory is always a contradiction. The development of modern electromagnetics requires numerical methods can solve larger scale and more complex problems. However, classical numerical computational methods are very difficult to meet with the memory and computational time requirements when solving these problems. This desseration is concerned with the solution of boundary value problems based on vector Helmholtz equations in electromagnetics and researches fast simulation techniques based on tangential vector finite element methods, mainly focuses on the fast simulation techniques that are used effectively in analyzing electromagnetic problems.At the beginning of the desseration, we briefly discussed and investigated the basic theory, current development status of the finite element method, then we briefly discussed the characteristic of the FEM system matrix and detailedly investigated a series of methods that are most appropriate for the solution of FEM linear systems, mainly including: preconditioning techniques based on the coefficient matrix, i.e. Jacobi preconditioning, SSOR preconditioning, FSAI preconditioning, diagonal perturbed IC preconditioning, etc; preconditioning techniques based on specific physical modes, i.e. preconditioning techniques based on the scalar and vector potential formulation or on the shifted Helmholtz operators; parallel domain decomposition methods for solving super large problems; efficient solvers based on hierarchical high order TVFEM, such as the ptype multigrid method, the Schwarz method, etc. Among these methods, preconditioning techniques based on coefficient matrix are suitable for general sparse matrices and have wide applications, preconditioning techniques based on specific physical models aims at the elimination of illconditioning component to construct the preconditioner, so that it can achieve high efficiency. Parallel domain decomposition methods use distributed memory computer to solve problems, which can solve some super large physical problems with reasonable costs. The application of high order basis is an efficient method to increase computational precision and decrease the number of unknowns when solving large problems, which is a new development direction of FEM. When these methods are applied in FEM simluations, they can effectively increase the efficiency of FEM to deal with large and complex problems. In this desseration, we analyzed and compared the efficiency of these methods in high frequency electromagnetic analysis in combination with the waveguide discontinuity and microstrip antenna problems, and proposed some new techniques in the analysis of electromagnetic problems, which can achieve superior efficiency.

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CLC: > Industrial Technology > Electrotechnical > Fundamental Theory of Electrical Engineering > The application of electromagnetic theory
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