Basic Research Of MPSTD Algorithm For Radiation Problems

The MPSTD algorithm has gone through 12 years of development since it was first put forward at the international symposium of AIAA by A. V. Kabakian in 1996. To solve the same equation, Maxwell's equations in forms of differential, MPSTD is much more than a improvement of FDTD. It has its own set of algorithms mechanism. The grids location differ from the Yee's cell in FDTD, and the time integration differs from the first-order central difference method. Through the domain decomposition, it makes the computing model conform with the border of the goals perfectly. The MPSTD method can break the bottlenecks of the time-domain algorithm, and its most prominent feature is that it can obtain high-order accuracy with low-density sampling, and is suitable for the analysis of electrically large problem.Despite the MPSTD algorithm has been widely used in the scattering problem, analysis of the waveguide and underground target detection. However, for the entire algorithm system, its analysis of the characteristics of the antenna's radiation would be a very useful supplement. This dissertation had a detailed study of a number of key technologies for the MPSTD algorithm, including the chebyshev collocation method, the high-order time-integration, the subdomain conformal and the subdomain patching. In the analysis of the characteristics of the antenna's radiation, aimed at the truncation and radiation boundary, had a research on the perfectly matched layer and the near to far-field transformation. The main work can be summarized as follows:(1) For the Runge phenomenon existed in the Lagrange's interpolation based on the equal space target points, introduced the superiority of Chebyshev polynomial interpolation approximation, and made a display of Chebyshev collocation method in solving partial differential with precision spectroscopy. This is the basis for spectral method.(2) Had a system research on the single domain Chebyshev pseudospectral time-domain algorithms. Deduce d the Maxwell's equations in the curvilinear coordinate. Had a Discusse on the regional mapping technology and high-order time-integration method, M-stage N-order Runge-kutta scheme. To verify the correctness of the theory, the single domain Chebyshev pseudospectral time-domain algorithm is applied to solve the resonant frequency for metal resonator .(3) Had a in-depth discussion of the multidomain Chebyshev pseudospectral time-domain algorithm. After a study on the CV-Patching and the PB-Patching between two adjacent subdomains, described how to exchange information by weekly imposing upwind numerical flow at the interface of two subdomains. Derived the explicit expression of the six field components at the interface node in the curvilinear coordinate. (4) In order to analysis of the radiation problem, UPML was brought into the MPSTD algorithm, and the approach of time integration is improved to meet the Runge-Kutta method. Had a detailed presentation on how to achieve near to far-field transformation in MPSTD algorithm. Made an analysis of the deficiencies in calculating the tangential surface current and the tangential surface magnetic current on the equivalent surface by average method, and gave out an improved manner in the following work plans.(5) Made a pattern analysis of several typical line-antennas and surface-antennas. Showed the effectiveness of the MPSTD algorithm in the analysis of the antenna's radiation.