(1. 中南大學(xué) 地球科學(xué)與信息物理學(xué)院，長(zhǎng)沙 410083；
2. 有色資源與地質(zhì)災(zāi)害探查湖南省重點(diǎn)實(shí)驗(yàn)室，長(zhǎng)沙 410083；
3. 中國(guó)海洋大學(xué) 海洋地球科學(xué)學(xué)院，青島 266100)
摘 要: 本文實(shí)現(xiàn)了基于有限元法的頻率域可控源三維正演并行算法。首先從麥克斯韋方程出發(fā)，推導(dǎo)出電場(chǎng)雙旋度方程及其邊值問題，采用廣義變分原理建立泛函并推導(dǎo)出有限元方程，并利用改進(jìn)的對(duì)稱逐步超松弛迭代方法(SSOR-PCG)來求解大型線性方程組。針對(duì)頻率域電磁法三維有限元數(shù)值模擬計(jì)算速度慢、各頻點(diǎn)計(jì)算相互獨(dú)立的特點(diǎn)，選用MPI并行技術(shù)，實(shí)現(xiàn)了基于頻點(diǎn)的對(duì)等并行算法。然后利用本文算法對(duì)均勻半空間模型進(jìn)行模擬計(jì)算，并將計(jì)算結(jié)果與解析解對(duì)比，驗(yàn)證了算法的準(zhǔn)確性和有效性。最后對(duì)模型實(shí)例進(jìn)行模擬，模擬結(jié)果均能在不同程度上反映出異常體，計(jì)算效率基本上能夠跟計(jì)算核心數(shù)成正比，從而說明了本文算法能夠?qū)︻l率域可控源電磁三維正演進(jìn)行有效地模擬。
關(guān)鍵字: 三維；頻率域可控源電磁法；有限元法；MPI；并行計(jì)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
