Multiresolution Time-Domain Method In Electromagnetic Field Computation

In this paper,we study the multiresolution time-domain(MRTD)method.In order to solve the transmission line problems and electromagnetic scattering problems,we derive the MRTD schemes based on Daubechies' scaling functions,and study the stability conditions and dispersion properties of the proposed MRTD schemes.The numerical results demonstrate the effectiveness of the proposed algorithm.The study in the paper widen the scope MRTD method and develop the boundary condition theory of this method.It has significant meaning for the using of MRTD method in electromagnetic compatibility(EMC)problems and electromagnetic scattering problems.The main contents of the paper include:First,in this paper,we introduce the MRTD method to the multiconductor transmission line problems.We derive the stability condition of MRTD method in one dimension problems and analyze dispersion properties of the schemes.The numerical results show that the discretization error of MRTD method is smaller than that of finite difference timedomain(FDTD)method under the same size grid.We propose a method the obtain the iterative equations of the terminal based on linear network loads.This method can be widely used in various kinds of network terminals.Numerical results prove the effectiveness of the MRTD method for transmission line problems.And the numerical results also show that using MRTD schemes to simulate the fast signal is more stable than the FDTD method.Second,different from the FDTD method in the electromagnetic scattering problems,the connecting boundary and absorbing boundary of the MRTD methods will become a region.It is no longer a side or a plane in the MRTD method,which is called the connected region and the absorbing boundary region.For the problem of two-dimensional scattering field,the modified form of the iterative equation in the boundary region is derived.The scheme makes full use of the results of the original iterative equation,which simplifies the calculation process and programming difficulty.In the region near the boundary of the computational region,the degenerate region is established,and the degenerate form of the MRTD method is proposed.In this region,the MRTD format will gradually degenerate into FDTD format,which can both reduce the calculation of the region and also allow the absorbing boundary conditions of the FDTD method into MRTD method In addition,the establishment of the degradation region can also solve the problem of exceeding the index in the MRTD method.Numerical results prove the effectiveness of the MRTD method for degenerate schemes.Third,in the three-dimensional electromagnetic scattering problem,the calculation regions and the iterative equations in each region are very complex.Therefore,for the three-dimensional scattering problem,we propose the filed split technique for MRTD methods.Based on the idea of Berenger field splitting,the iterative equation of each electromagnetic component is split.At the same time,the original computing regions are also split.The calculation regions are simpler than the original calculation regions and the distribution of the regions are more regular.Split field and its computational region,the form of the iterative equation will be relatively simple in the connected boundary region and the degenerate region.It is easier to derive the iterative equations and program in computer by the symmetry of the computational region and the iterative equation.