Basic equations of electromagnetic are Maxwell equations. In this manuscript, ADI-IRBF-GMLS is employed for solving the time-dependent Maxwell equations in two-dimension. For approximating the time variable, we utilize alternative direction implicit (ADI) method and integrated radial basis function based on generalized moving least squares (IRBF-GMLS) method is used for space direction. Alternative Direct Implicit (ADI) technique includes two steps in each time stage, that their computations are simple. We have to increase the number of collocation points and also time steps to reach the final time. This procedure increases the used execution time. To overcome this issue, we employ the proper orthogonal decomposition (POD) method to reduce the size of the final algebraic system of equations. This numerical procedure can be called ADI-IRBF-GMLS-POD method. Numerical results are presented and they illustrate the accuracy and efficiency of the proposed method. The point to note is that the used time-discrete scheme i.e. ADI approach cannot be employed in the numerical simulations on non-rectangular computational domains for solving Maxwell equations. This is the main issue in this numerical approach for Maxwell equations. We also compare the ADI-IRBF-GMLS with POD with full model of presented method applied to solve Maxwell equations.

电磁的基本方程是麦克斯韦方程。在这份手稿中，ADI-IRBF-GMLS 用于求解二维时间相关的麦克斯韦方程。为了逼近时间变量，我们利用交替方向隐式（ADI）方法和基于广义移动最小二乘法（IRBF-GMLS）的集成径向基函数用于空间方向。替代直接隐式（ADI）技术在每个时间阶段包括两个步骤，它们的计算很简单。我们必须增加搭配点的数量和时间步长才能到达最终时间。此过程会增加使用的执行时间。为了克服这个问题，我们采用适当的正交分解（POD）方法来减小最终代数方程组的大小。这个数值过程可以称为 ADI-IRBF-GMLS-POD 方法。给出了数值结果，它们说明了所提出方法的准确性和效率。需要注意的一点是，所使用的时间离散方案（即 ADI 方法）不能用于求解麦克斯韦方程组的非矩形计算域的数值模拟。这是麦克斯韦方程的这种数值方法中的主要问题。我们还将 ADI-IRBF-GMLS 与 POD 与应用于求解麦克斯韦方程的所提出方法的完整模型进行了比较。这是麦克斯韦方程的这种数值方法中的主要问题。我们还将 ADI-IRBF-GMLS 与 POD 与应用于求解麦克斯韦方程的所提出方法的完整模型进行了比较。这是麦克斯韦方程的这种数值方法中的主要问题。我们还将 ADI-IRBF-GMLS 与 POD 与应用于求解麦克斯韦方程的所提出方法的完整模型进行了比较。