Study On Two-Dimensional Multi-domain Pseudospectral Time Domain Method

The multi-domain Pseudospectral time method (MPSTD) was brought into computational electromagnetics in late 90's last century. Some problems in MPSTD have not be solved efficiently and the method has not be applied widely because this method has not developed for a long time. In this paper, Chebyshev pseudospectral time-domain method is studied systematically base on the previous works of other researchers.First, the single domain Chebyshev pseudospectral time domain method is studied. The superiority of the Chebyshev polynomial interpolation approximation is introduced and Chebyshev matching method has high accuracy in partial differential solution. The Maxwell's equations were derived under the curvilinear coordinates. The transformation of curved quadrilateral from the Cartesian coordinate system to the unit square coordinate system was discussed. The common type of excitation sources and the implementing method were studied and Runge-kutta method was also studied.Then the multi-domain Chebyshev pseudospectral time domain method is systematically studied. Three kinds of matching conditions between the sub-domains, characteristics of the variable sub-domain matching conditions, matching the physical boundary matching conditions, characteristics of the variable-physical boundary conditions, are introduced and field components expressions at the interface are derived by the three methods. Two absorbing boundary conditions, absorbing boundary conditions based on characteristic variables, well-posed PML are discussed and selected to truncate calculating boundary in the MPSTD method. Finally, examples were computed to shown the effectiveness of the MPSTD compared with the FDTD algorithm.