The Application Of FDTD Method Used In Scattering Problems

The FDTD (Finite-difference Time-domain) method, which is based on differentialform of Maxwell’s equations, is a significant part of numerical calculation ofelectromagnetic fields and can effectively solve problems of electromagnetic. FDTDmethod has had been used in many fields currently and a great many excellent resultshas had been achieved. As for Electromagnetic scattering problems, because of itsfunction in engineering applications, it attracts much attention. Researches aboutscattering problems also become hot field in numerical calculation.Firstly, some key problems in FDTD are studied in this paper. Maxwell’s equationsare discretized in terms of Yee lattice, the numerical dispersion of FDTD algorithm iseffectively suppressed by Courant stability condition, also the problem space isrestricted to a limited scale by PML absorbing boundary condition. Besides, padéalgorithm is introduced to simplify the procedure of PML in favor of avoiding theoccurrence of some errors.To calculate the Radar Cross Section, two important issues, that the introduction ofplane wave and the acquisition of far field information, are then discussed. According tothe connective boundary condition, plane wave is introduced exactly by fixing theequations of the fields, which locates near the boundary. The information of far field isthen achieved by the way of near-to-far field transformation on the basis of equivalenceprinciple. Examples of calculating RCS are given afterwards, verifying the effectivenessof the two algorithms in the application.Traditional FDTD method has only second order accuracy both in spatial andtemporal domain, whereas generalized higher order algorithm can improve the accuracy.By applying the discrete singular convolution, precision in spatial domain can be raisedto2M, while difference accuracy in temporal will be improved up to fourth order afterusing symplectic integrator propagator. Some formulas of PML and connectiveboundary condition are derived to satisfy the (2M,4) higher order algorithm. Then thehigher order algorithm is successfully used in two-dimensional and three-dimensionalscattering problems. To resolve the conflict between calculation precision and storage space,non-uniform FDTD method is paid attention to. The subgridding method called localgrid with material traverse is quite effective for local refinement. When this subgriddingway is applied, the obtained result is consistent with that gotten when all fine mesh usedin space. When the non-uniform method based on step summing coordinatetransformation is introduced, storage space and calculation time can be effectively saved,higher precision can also be achieved meanwhile. The coordinate transformationfunction is flexible and applicable for both traditional FDTD and (2M,4) generalizedhigher order algorithm, by using this method good simulation results are also achieved.