Absorbing boundary conditions in leapfrog ADI-FDTD method

摘要

In this paper, the performance of the absorbing boundary conditions (ABC's) in leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method is investigated in detail. In the leapfrog ADI-FDTD method, the ABC's must be applied to both the electric and magnetic field. The performance of the ABC's are different from it in other FDTD methods. Thus, it is necessary to identify the absorbing performance and numerical stability and construct better performance ABC's. In the second part, an ABC is constructed with three points adjacent to the boundary. Then, in the third part, the absorbing performance and numerical stability of the proposed ABC and some other conventional ABC's are analyzed with numerical examples. The absorbing performance was studied by simulating the wave propagation in the free-space model in 2D case. The reflection error is calculated to compare these ABC's. It is shown that the propesed ABC have a similar maximum reflection error with the first order Mur's ABC. Then the Numerical stability is carried out in 3D case. It is found that the conventional Mur's ABC has the long time instability problem in the leapfrog ADI-FDTD method. However, the proposed ABC performs better for good stability in leapfrog ADI-FDTD mehtod.