A 3-D fourth-order one-step leapfrog HIE-FDTD method with CPML

Abstract

ABSTRACT A 3-D fourth-order one-step leapfrog HIE-FDTD method with convolutional perfectly matched layer (CPML) has been proposed in this paper. When the time step size satisfies with the time stability condition, the maximum reflection error of the proposed method is below −79 dB, which demonstrates good absorbing performance of the CPML method. To verify the accuracy, we give the numerical dispersions analysis of the proposed method with the traditional FDTD method and the traditional HIE-FDTD method. The results demonstrate that when the time step size of the new method is the same with the other methods, the proposed method has the smallest dispersion error. Besides, numerical examples demonstrate that the proposed method spend much less CPU time than the traditional FDTD method and the traditional HIE-FDTD method. Last but not least, simulations for thin slots present that the proposed method is very useful to solve problems with coupled field.