Study On The Applications Of Domain Decomposition Method In Electromagnetic Problems

On the base of mathematical domain decomposition method (DDM), this paper investigates systematically the quasi-static problems based on Laplace equation, the transmission problems in waveguide based Helmholtz equation and the three-dimensional scattering and radiation problems based on Maxwell equations. The theoretical system is built for the further exploration of DDM in electromagnetic problems.At first, the relaxed iterative Schwarz alternating method based on the Laplace equation is discussed. Then through the DDM, the method of lines (MoL) combined with the finite-difference frequency-domain (FDFD) method is used for the parameter extraction of multilayered multiconductor interconnections. The subregion with pure dielectric layers is analyzed by MoL and the fast Fourier transform (FFT) is introduced to reduce the computing time, while the subregion with conductors is analyzed by FDFD to take advantage fully the superiorities of these two methods. As the subregion with pure dielectric layers is analyzed by MoL. the computing time is unrelated to the thickness of the pure dielectric layers. In view of engineering, the effect of the uneven dielectric division on the electromagnetic parameter is also investigated. The FFT of Laplace equation on the regular domain is studied. As the application, combined with DDM, the fast algorithm is used to compute characteristic impedance of rectangular coaxial line.Secondly, the physical nature of divergence of iterative DDM based on the Schwarz alternating method in treating waveguide problems is given in this paper. Also an absorbing fictitious boundary condition (FBC) is presented to generate an iterative DDM for waveguide problems. The FBC for connecting the subdomains on fictitious boundary is developed according to the actual field distribution in the waveguide to ensure the propagation of waves between adjacent subdomains. The relaxed algorithm is introduced to improve the iterative convergence. The FFT of Helmholtz equation on the regular domain is studied. And the multifrontal algorithm is used to solve the matrix equations in computational electromagnetics.Finally, the finite-difference approximate forms of Maxwell equations and the Despres transmission condition are discussed. The novel three-dimensional finite-difference approximations of Mur's absorbing boundary conditions are also presented in frequency-domain. Then the DDM based on FDFD is investigated in the applications of three-dimensional electromagnetics problems. And it is used to analyze the leaky wave antenna based on image nonradiative dielectric (NRD) guide.