High Precision Numerical Method For Plasma Electromagnetic Field Modeling

In daily life,plasma materials have been widely used in military,medical,food safety,garbage disposal and other fields.The calculation of the plasma electromagnetic field is one of the important methods for plasma theory and application research.Because of the plasma Maxwell's equations,it is very complicated to solve the equations for different structures and different boundary conditions,and numerical methods are required.With the rapid development of electronic computer technology,there have been many methods to solve the electromagnetic field in time domain,finite difference time domain method is one of the most commonly used methods.In the calculation of the electromagnetic fields in plasma,in order to improve the accuracy of numerical results,it is necessary to develop numerical algorithms having high precision in time and space.This paper studies the higher-order numerical schemes and numerical analysis for the Maxwell's equations with plasma in time domain.The following work is completed in this paper.1.Under the periodic boundary conditions,for the two-dimensional Maxwell's equations in plasma,a second-order alternative direction implicit finite-difference time-domain method is proposed.The discrete energy method is used to give a priori estimate in the maximum norm of the scheme.Basing on it,the unconditional stability and the second-order convergence both in time and space are demonstrated.In order to improve the accuracy of the numerical results,the Richardson extrapolation is applied to the proposed scheme and the resulting algorithm is of fourth-order accuracy both in time and space.2.The higher-order approximation of the exponential operator and the operator splitting technique are used to develop the alternating direction implicit finite-difference time-domain method which has fourth order convergence in time.Numerical experiment verifies that the proposed scheme is of second-order accuracy in space and fourth-order accuracy in time.3.The compact finite difference technique is used in the spatial directions to construct the spatial compact alternating direction implicit finite-difference time-domain.Numerical example confirms that the extrapolated algorithm has fourth-order accuracy both in time and space.The three higher-order numerical schemes proposed in this paper are all unconditionally stable and large time step could be taken in practical computation to achieve high efficiency.