Investigation Of The FDTD Method For Electromagnetic Field

In the computation of electromagnetic field, we cannot get the accuratesolutions. Only several numerical solutions can be widely used. In the famouspaper "Numerical Solution of Initial Boundary Value Involving Maxwell'sEquation in Istropic Media"written by Kane S .Yee in 1966, Kane S. Yee usedspatial discrete method(Yee's grid) transformed the Maxwell's equations withthe time variables into finite difference equations, This method became a newmethod of electromagnetic solution which we called "Finite-differenceTime-domain method"(FDTD) later.After more than thirty years of improving, the FDTD method becomes moreeffectively. However the conventional FDTD method has some errors. Theerrors mainly comes from the accuracy error of finite-difference, the reflect errorof the absorbing boundary condition, the numerical dispersion caused by thephase velocity, the error caused by the variable cross sections surface of theenmeshment when modeling scattering objects surface, the error caused by theloaded-wave-source and the truncation error caused by the numerical valueoperations. In this paper, we begin with the problems of the absorbing boundarycondition, take into account of the magnetic component in the calculations toreduce the reflect error caused by the nonphysical factors when calculating theelectric component. We proved that it has improved the accuracy of the absorbingboundary condition and can reduced the reflect coefficient by theory at mostangles of incidence.First in this paper, we have given the finite-difference equations from theMaxwell's equations and derived the FDTD equations in cylindrical coordinatesystems, discussed the relations between the stability of the FDTD numericalsolution and the step of time and spatial, introduced several source of the FDTD,and discussed the set-up of the excitation source of scattering problems. The electromagnetic field is an "open system", so we usually assume thespace is infinite. But when we use FDTD method, we are often limited by thestorage and calculation speed of the computer. So we should put the discussedobject into finite spatial, and then we can use FDTD methods to calculate. In orderto keep this finite spatial equals to infinite spatial, we need use special method totreat the finite spatial, so that the wave propagating to outside border remainoutside-propagating at the boarder, and has low reflect. The boarder has thisfunction we called "Absorbing boundary condition". Absorbing boundary hasmany style, in this paper we derivate the difference schemes of Mur first-orderand second-order absorbing boundary conditions in cylindrical systems. In the calculation of FDTD, we are often limited by the storage of thecomputer, can only get the near-field characteristic of the discussed problems. Butsometimes we need know the far-field characteristic, so we should transform thenear-field characteristic to far-field characteristic. In this paper, we transformed itin frequency-domain and time-domain two ways use field equivalence principle.Then we can get the far-field characteristic of the discussed problems. The conventional absorbing boundary conditions such as Mur absorbingboundary conditions which has been used widely now also have many defects:The reflect coefficient is not very low, and it's use is also limited by the angle ofincidence which is not too wide. In this paper we improved the algorithm of theconventional method, The conventional absorbing boundary conditions onlycalculate the Ez component at i=M grid point by the given special difference...