【作者】 赵斯晗； 魏兵； 何欣波；

【Author】 ZHAO Sihan;BING Wei;HE Xinbo;School of Physics and Optoclectronic Engineering,Xidian University;Collaborative Innovation Center of Information Sensing and Understanding,Xidian University;

【机构】 西安电子科技大学物理与光电工程学院； 西安电子科技大学信息感知技术协同创新中心；

【摘要】 本文将周期边界条件(Periodic Boundary Condition,PBC)引入到了显式无条件稳定时域有限差分方法(Unconditionally Stable Finite Difference Time Domain,US-FDTD)中。这一过程是通过改变系统矩阵中面片和棱边的耦合关系实现的。具体步骤为:首先根据Floquet定理,找到周期边界外的磁场场量在计算域内等效磁场的位置;之后确定等效磁场对应的面片编号;再修改矩阵中对应位置的元素,最后将修改后的矩阵代入迭代计算。数值算例说明了该引入方法的正确性和用US-FDTD方法计算周期结构问题的优越性,为以后用US-FDTD方法分析复杂周期结构的电磁问题奠定了基础。更多还原

【Abstract】 In this paper,the periodic boundary condition(PBC) is introduced into the explicit unconditionally stable finite difference time domain(US-FDTD) method.This scheme is realized by changing the coupling relationship between patches and edges in system matrix.The specific steps are as follows.Firstly,according to the Floquet theorem,we can find the position of corresponding magnetic fields inside the domain,which is equivalent to the magnetic fields outside the boundary.Then the patch number corresponding to the equivalent magnetic field can be obtained.After that,the elements of the corresponding position in system matrix are modified.Finally,the modified matrix is substituted into the field iteration.Numerical results show the correctness of the proposed scheme and the superiority of US-FDTD in calculating the problem of periodic structures,which lays a foundation for US-FDTD in solving electromagnetic problems of complex periodic structures in the future.更多还原