基于非重叠区域分解算法的大地电磁法二维正演模拟  

Non-overlapping Domain Decomposition Method for Two-dimensional Magnetotelluric Forward Modeling

作　　者：赵航 陈辉[1] 邓居智[1] 李丹[1] 余辉[1] ZHAO Hang;CHEN Hui;DENG Ju-zhi;LI Dan;YU Hui(Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense,East China Institute of Technology,Nanchang330013,China)

机构地区：[1]东华理工大学放射性地质与勘探技术国防重点学科实验室

出　　处：《科学技术与工程》2019年第25期24-32,共9页Science Technology and Engineering

基　　金：国家自然科学基金青年基金(41404057);国家自然科学基金(41164003,41674077)资助

摘　　要：区域分解算法采用分而治之的思想,将大规模问题转化为若干个小问题进行求解,已成为大规模数值计算领域的常用算法之一。将非重叠区域分解算法引入到大地电磁法二维正演模拟中。首先将整个求解区域分解为多个互不重叠的子域,子域之间共享边界元素;然后对每个子域采用有限差分进行离散,采用Schur补偿算法解耦得到共享边界节点上的未知数,并作为子域问题的边界条件得到关于子域内部节点的线性方程组;最后,利用直接求解算法对上述方程组进行求解,实现了大地电磁法二维正演。该算法的准确性和可行性通过多个地电模型的对比试算得到了验证。此外,还统计分析了采用不同子域分区方式和分解个数时的计算耗时,结果表明子域分区的方式对计算效率影响不大,但子域分解个数的影响则较大,进行区域分解时需要选择合适的子域个数。Domain decomposition method uses the idea of divide and conquer,which transforms large-scale problem into several small problems to solve,and becomes one of the frequently used methods in the field of largescale numerical computation. The non-overlapping domain decomposition method was introduced into the two-dimensional forward simulation of magnetotelluric. Firstly,the whole domain was decomposed into several non-overlapping subdomains,and the boundary elements were shared between subdomains. Then,every subdomain was discretized by finite difference method,the unknowns on shared boundary nodes were decoupled by Schur compensation algorithm,and as boundary conditions of sub-domain problems,a set of linear equations about nodes in subdomain were obtained. Finally,the direct solution method was used to solve the problem,thus the two dimensional forward modeling of magnetotelluric was realized. Through numerical simulation of several typical geo-electric models and comparison the feasibility and accuracy of this method are verified. In addition,comparing the effects of regular subdomain division and irregular subdomain division,and studying the influence of the number of subdomain. The results show that whether the shape of the subdomain is regular or not has little effect on the computational efficiency,but the number of subdomains has a great influence on the computational efficiency,so select the appropriate subdomain number is necessary.

关 键 词：大地电磁法 非重叠型区域分解 Schur补偿算法 正演模拟 

分 类 号：P319[天文地球—固体地球物理学] P631[天文地球—地球物理学]