Research On The Computational Errors And Dispersive Media Model For Finite-Difference Time-Domain Method

Finite-Difference Time-Domain(FDTD)method has been widely studied and applied in computational electromagnetics,.It has become a mature method to solve engineering electromagnetic problems.However,with the deepening of the application of FDTD method and the expansion of its application scope,the simulation complexity and scale of electromagnetic problems have multiplied,there are some new problems and challenges.Usually with parallel computing to solve the problem of insufficient computing resources caused by the increase of simulation scale,which can improve computing efficiency.However,as the main parallel computing devices,graphics processing unit(GPU)and field programmable gate array(FPGA)have excellent single-precision computing performance,but it is difficult to meet the redundancy requirements of double-precision computing.Therefore,it is necessary to analyze and study the reliability of FDTD method with single-precision computing.Moreover,because resonance effect is related to dielectric properties of dielectrics,it is necessary to accurately model the dielectric properties of dispersive medium when FDTD method is applied to the study of SPR and other micro-nano composite structures.Based on the above problems,the computational reliability and error characteristics of FDTD method are discussed in this paper.The main research contents of this paper are as follows:Firstly,the basic principle of FDTD method,the storage format and operation method of floating-point calculation in computer are introduced.The FDTD method is classified according to algorithm error,calculation error in single precision mode and dispersion material model error.The causes of error are explained respectively.Secondly,the accuracy of absorbing boundary,excitation source and electromagnetic wave propagation under single-precision computing is verified by an example set by programming.Comparing the results of single-precision and double-precision computing,we can draw a conclusion that:Because of the space-time locality of FDTD method,in the case of mesh refinement,if the difference of field values between adjacent meshes in the iteration time step is less than the range of single-precision computing numerical representation,then the single-precision computing of FDTD method is reliable,and there is no difference with the double-precision computing.Therefore,it is feasible to implement FDTD method on the current popular GPU and FPGA single precision parallel platform,which can greatly improve the efficiency of electromagnetic simulation.Finally,the modeling processing methods of dielectric properties of dispersive media in FDTD method are systematically expounded.Then,in a specific frequency band,the traditional Drude model is modified by using the critical point(CP)approximation,and the modified model is integrated into the FDTD method by using the Auxiliary Differential Equation(ADE)method.Then the Drude 2CP model is written into the software named FDTD Solutions as a plug-in.An example of enhanced transmission phenomena is used to analyze the problems caused by the use of the Drude model,and the correctness of the modified model in the wavelength range of 200 nm to 1000 nm is verified.