一种新的角点条件

摘要

Mur角点条件是时域有限差分法(FDTD)的一种常用角点条件,但人为的假设波在角点附近沿角点所在网格的对角线传播,这在很多情况下与实际不符,存在较大误差.提出了一种新的角点条件,其基本原理是:把波的单向波方程在波的实际传播方向上差分离散,而不是像Mur角点条件那样在角点所在网格的对角线上差分离散,这样就可能需要用到某些非网格节点上的场值,用到的非网格节点上的场值由周围的网格节点上的场值线性插值得出.为了验证这种角点条件的有效性,编程进行了数值实验,实验结果表明新角点条件的吸收效果好于Mur角点条件.%Mur vertex condition is a common vertex condition of the finite difference time domain method ( FDTD) , but it assumes that the waves near the vertexes propagate along the diagonal lines of the grids which the vertexes are located in. The assumption is incorrect and results in larger error in many cases. A new vertex condition is brought forward, and the fundamental principle of the condition is as follow: The one-way wave equations of the waves are differenced along the actual propagation directions of the wave, but not along the diagonal lines of the grids which the vertexes are located in, like Mur vertex condition. The condition may need field values of some points that are not the knots, and the values can be got by linear interpolation based on the values of the knots which are near the points. In order to verify the validity of the condition, numerical experiments were done, and the experiment results indicate that the absorbing effects of the condition are better than the absorbing effects of Mur vertex condition.