时域有限差分法的收敛性

The Convergence of the Finite—Difference Time—Domain (FD—TD) Method

本文通过计算实例讨论了时域有限差分法的收敛性问题。计算了在平面波照射下无限长介质柱中的电磁场分布。把不同空间和时间步长时的计算结果,与用解析法所获得的结果进行比较,证明时域有限差分法有较好的收敛特性。对具有不同空间分辨率的人体二维非均匀块状模型中吸收电磁能量分布的计算表明,在高度非均匀介质中的场分布,仍然保持较好的收敛性。这些讨论从一个侧面提供了选取网格步长的依据。

This paper discusses the convergence problem of the Finite—Difference Time—Domain (FD—TD) method through some computing examples. The electromagnetic field distribution in an infinite dielectric cylinder illuminated by plane wave have been calculated and the results of calculation with various space steps and time steps are compared with their analytical results. It shows that the FD—TD method has a good convergence performance. EM energy distiribution absorbed by a two dimensional nonuniform man block model with different space resolution has been calculated and it shows that the EM distribution still has good convergence, even for highly nonuniform medium. These discussions provide the basis in one aspect for selection of the steps of the meshes.