The Research On 3-D ADI-FDTD Method And WCS-FDTD Method

The thesis aims to do some research on Alternating Direction Implicit Finite Difference Time Domain method (abbreviation ADI-FDTD method) and Weakly Conditional Stability Finite Difference Time Domain method (abbreviation WCS-FDTD method).The paper firstly reviews and elaborates Finite Difference Time Domain method (abbreviation FDTD method), then compares the calculation results with the simulation results of HFSS commercial software and classical theory, eventually verifies that traditional FDTD method is correct and accurate.However, traditional FDTD method is confined to the Courant stability condition, so unconditonally stable ADI-FDTD method has been researched in this thesis. The unconditional stability of three-dimensional ADI-FDTD method is proved, and the three-dimensional metal resonant cavity structures, microstrip inset-fed patch antenna as well as band trap filter are analyzed. It can be perceived that with appropriate augmentation of time step size, ADI-FDTD method is able to shorten calculation time and raise calculation efficiency, while sustaining the calculation precision. Nevertheless, the numerical dispersion error is getting higher with the augmentation of the time step size in ADI-FDTD method, finally leading to higher calculation error.Besides, the calculation in ADI-FDTD method is complex, the calculation efficiency is merely raised relative to FDTD method. In this case, the WCS FDTD method with stability of weak conditions is studied. The thesis detaily deduces the difference equation of three-dimensional WCS-FDTD method, and proves the weakly conditional stability of three-dimensional WCS-FDTD method: the time step is only related to one arbitrary space step, while the other two direction space steps are irrelevant. The paper appropriately introduces UPML absorbing boundary condition into WCS-FDTD method, and analyzes three calculation example of ADI-FDTD method. Which verifies that with the same time step size, the calculating time of WCS-FDTD method is about 70% of that of ADI-FDTD method, also the calculation efficiency and calculation accuracy are better. Furthermore, through calculating and analyzing winding type microstrip structure, it can be proved that while dealing with electromagnetic problem of bigger space step size, WCS-FDTD method is of higher calculation efficiency and better utility value.