(1. 中南大学 地球科学与信息物理学院，长沙 410083；
2. 有色资源与地质灾害探查湖南省重点实验室，长沙 410083；
3. 中国海洋大学 海洋地球科学学院，青岛 266100)
摘 要: 本文实现了基于有限元法的频率域可控源三维正演并行算法。首先从麦克斯韦方程出发，推导出电场双旋度方程及其边值问题，采用广义变分原理建立泛函并推导出有限元方程，并利用改进的对称逐步超松弛迭代方法(SSOR-PCG)来求解大型线性方程组。针对频率域电磁法三维有限元数值模拟计算速度慢、各频点计算相互独立的特点，选用MPI并行技术，实现了基于频点的对等并行算法。然后利用本文算法对均匀半空间模型进行模拟计算，并将计算结果与解析解对比，验证了算法的准确性和有效性。最后对模型实例进行模拟，模拟结果均能在不同程度上反映出异常体，计算效率基本上能够跟计算核心数成正比，从而说明了本文算法能够对频率域可控源电磁三维正演进行有效地模拟。
关键字: 三维；频率域可控源电磁法；有限元法；MPI；并行计算
（1. School of Geosciences and Info-physics, Central South University, Changsha 410083, China;
2. Hunan Key Laboratory of Non-ferrous Resources and Geological Hazard Detection, Changsha 410083, China;
3. Ministry of Education and College of Marine Geosciences Ocean University of China, Qingdao 266100, China）
Abstract:In this paper, a parallel algorithm of the three-dimensional(3D) modeling of frequency domain controlled-source electromagnetic(FCSEM) with FEM was implemented. First, from the Maxwell equations, its boundary value problem was derived, and then transformed into variational form from which finite-element linear equations were derived. The SSOR-PCG iterative method was used to solve large-scale linear equations. Aiming at the low speed of 3D finite element numerical simulation of electromagnetic field in frequency domain and the independent calculation of each frequency, MPI parallel technology was adopted to realize the parallel algorithm based on frequency point. Then the algorithm was used to simulate the uniform half space model, and compared the calculated results with the analytical solutions to verify the accuracy and validity of the algorithm. Finally, the example model was simulated with three-dimensional electromagnetic responses. The results indicate that the method can be applied for solving three-dimensional electromagnetic responses. The algorithm has been demonstrated, which can be effective to modeling the geo-electrical structures.
Key words: three-dimensional; FCSEM; finite element; MPI; parallel computing
