Study On Finite - Difference Time - Domain Finite Difference Method

Finite-difference time-domain method (FDTD) has been widely used to simulate the electromagnetic scattering and radiation problems because of its simple mathematical process and the high efficiency. The conventional FDTD will introduce staircasing error in analysing curved objects. Conformal technique and subgridding technique are proposed to reduce the staircasing error.The chief shortcoming of conformal finite-difference time-domain method (CFDTD) is the global time-step reduction to avoid instability arising from small irregular cells, A new scheme has been used to overcome this problem. The time-step reduction is applied only in irregular cells and the time-step can be chosen according to the conventional Courant-Friedrichs-Lewy in regular cells, so the simulation time is less than conventional CFDTD. Sub-grid technology has advantage in handling a large area with a tiny structure or a dielectric with high relative permittivity inside. So it is easy to be considered that the advantages of both CFDTD and sub-grid technology can be combined.This thesis has focused on how to generate conformal-mesh through the structure information from ANS YS. Considering the shortcoming of the conformal CFDTD in dealing with perfect conducting curved objects, a new conformal scheme to overcome this problem through using the multi-scale time step processing has been introduced. The time-step reduction only applied in small irregular cells can save the simulation time obviously. Finally CFDTD are combined with sub-grid technology, which can be treated as using multi-scale technology in space. Numerical results have demonstrated its validity and efficiency in simulating the electromagnetic scattering problems.