This study presents a fast and efficient vector finite element method, based on the model reduction algorithm, to simulate the 3-D magnetotelluric response. Firstly, we derive a finite element governing equation based on electric field vector from Maxewell's equations Then we express the electric field by a function of frequency parameter to get a transfer function that can be approximated by the Krylov subspace model reduction algorithm. The transfer function after model reduction has far lower dimensions than the original one, and it can be directly solved by the Pardiso solver. Therefore, the computational efficiency is significantly improved. For validation, we compare the proposed algorithm with the 3-D direct finite element method (3DFEM) by a three-layer model, and the results show that the computation time of the former is less than 1/10 of the latter for the same accuracy. We also compare the electromagnetic response obtained by the proposed method with that obtained by two classical models, COMMEMI 3D-2A Model and Dublin Test Model 1. These results agree well, indicating that the proposed method is feasible and efficient for 3-D magnetotelluric forward modeling.

本研究提出了一种基于模型约简算法的快速有效的矢量有限元方法，以模拟3-D大地电磁响应。首先，从麦克斯韦方程组导出基于电场矢量的有限元控制方程，然后通过频率参数函数表达电场，得到可以用克雷洛夫子空间模型约简算法近似的传递函数。模型简化后的传递函数的维数远小于原始维，可以用Pardiso求解器直接求解。因此，大大提高了计算效率。为了进行验证，我们通过三层模型将提出的算法与3-D直接有限元方法（3DFEM）进行了比较，结果表明，在相同精度下，前者的计算时间小于后者的1/10。我们还比较了该方法所获得的电磁响应与两个经典模型COMMEMI 3D-2A模型和都柏林测试模型1所获得的电磁响应。这些结果吻合良好，表明该方法对于3D大地电磁正演是可行且有效的造型。