Research On Plane Wave Injection And Perfectly Matched Layer Based On High-Order FDTD

The finite difference time domain method(FDTD)is one of the main numerical methods for calculating electromagnetic field,which has been widely used in solving various electromagnetic field problems.Since the traditional FDTD scheme adopts second-order accuracy in both temporal and spatial central difference,the numerical dispersion will increase with the increase of the mesh resolution after dividing the largesize mesh,which will reduce the accuracy of the simulation results.This paper is based on the Conservative high-order Modified FDTD(2,4),which is a high-order FDTD scheme utilizing second-order and fourth-order differences in time and space respectively,focused on the plane wave injection and perfectly matched layer.When injecting a plane wave source,it is necessary to introduce a wave source with a low noise level,especially when simulating weak scattering problems.This paper proposes the split-field propagator based on CM24 scheme(SFP-CM24)to solve the leakage problem.At the same time,the absorption boundary is adopted to truncate the FDTD region for the open region problem.In this paper,the extension of the Convolution Perfectly Matched Layer based on CM24 scheme(CPML-CM24)is proposed based on the Convolution Perfectly Matched Layer(CPML).The CPMLCM24 matches the size of grid between the main grid and CPML to avoid the reflection caused by the mismatch of grid size which has a better absorption effect.Specific research work are as follows:1.Research on the CM24 scheme.The field update formula of CM24 scheme is derived in detail,with the numerical dispersion relation of CM24 scheme.The numerical dispersion relation derived by Newton iteration method is used to solve the numerical wave number,and then the coefficients of different loops by different resolutions are solved to minimize the numerical dispersion in the whole main grid.2.The Split-Field Propagator Based on CM24 scheme.Based on the CM24 scheme,the connecting boundary is added,with the injection of the incident plane wave.Focus on the large leakage problem in the scattered-field region of the traditional incident wave,SFP-CM24 is proposed.SFP-CM24 reduces the leakage problem in the scattered-field region by matching numerical dispersion relation and avoiding linear interpolation.In addition,the relative wave number errors of SFP-CM24 in various directions in the propagation space are analyzed in detail,with the analyzation in different incident angles on the numerical dispersion.Compared with the traditional one-dimensional incident wave,the accuracy of the proposed method is also verified by the three-dimensional numerical examples.3.The Convolution Perfectly Matched Layer Based on CM24 scheme.To solve the problem of the mismatches between the main grid and the absorption boundary,the CPML-CM24 is proposed.The field update formula of CPML-CM24 is derived in detail,with the optimization of corresponding parameters.Compared with the mixed convolution perfectly matched layer,CPML-CM24 has a smaller reflection effect at the boundary between the main grid and the convolution perfectly matched layer.