A Research Of DGTD Algorithm And The Related Parallel Computation Technologies

Discontinuous Galerkin Time Domain method(DGTD)is widely accepted as a promising method for solving multi-scale problems in the field of computational electromagnetics.Compared with traditional finite element methods,DGTD method introduces numerical flux to the formulation,imposes weakened condition of continuity between elements,thus gives it the capability of explicitly updating the electromagnetic field in every time step,just like Finite Difference Time Domain method.The DGTD method establishes updating formula within each element,avoids the difficulty of solving large sparse matrix equation of traditional finite element methods,tremendously increases the computational efficiency,making the method extremely suitable for massive parallel graphics computing.At the same time,Discontinuous Galerkin Time Domain method inherits all the advantages of finite element methods by allowing unstructured,conformal mesh to accurately model complex geometrical structures,and domain decomposition scheme to handle multi-scale problems.This thesis introduces some key technologies of DGTD method and the development of the simulation program,and its application in analysis of real electromagnetic problems.Besides,we analyzed the massive parallel computation technique of method of moment.Chapter 1 reviews some common time domain methods in computational electromagnetics,briefly compares them with DGTD method,and introduces the background of this research,and points out the meaning of this work.Chapter 2 introduces the key technologies of finite element time domain method and the fundamental theory of FEM and DGTD,studies the construction of nodal and edge basis function in tetrahedral element.Then is the finite element time domain formulation,which discretizes the equation in space in a similar manner with frequency domain method and then constructs time stepping formula from the ordinary matrix differential equation using central difference method,and excites the problem using kinds of time domain waveforms.Chapter 3 discusses the Discontinuous Galerkin Time-Domain method thoroughly.We introduces the basic idea of DGTD method from FETD,then analyzes its boundary condition and discrection scheme based on central flux and upwind flux DGTD.In the simulation of two three dimsional problem of electric dipole radiation and mode analysis of rectangle waveguide using the parallel implementation of the algorithm,we tested the accuracy and efficiency of the method and compared it with FETD and FDTD method.Chapter 4 researches the massive parallel computation technology of method of moment.Focusing on the analysis of electrically large millimeter wave antenna array in real project,we studied the parallel computation of impedance matrix and fast factoration of impedance matrix,tremendously increased the efficiency of solving electrically large problems.Chapter 5 summarizes the contents of this thesis and analyzes the prospect of our research.