基于Schwarz重叠型区域分解的大地电磁二维正演研究  

Overlapping Schwarz domain decomposition method for two-dimensional magnetotelluric forward modeling

作　　者：李丹[1] 陈辉[1] 邓居智[1] 

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,南昌330013

出　　处：《地球物理学进展》2017年第3期976-981,共6页Progress in Geophysics

基　　金：国家青年基金项目(41404057);国家自然科学基金项目(41164003;41674077)联合资助

摘　　要：区域分解算法将大规模问题转化成若干小问题进行求解,极大缩小计算规模和节省内存空间,已成为解决大规模复杂数值问题的有力手段.本文以大地电磁法(MT)二维正演为例,将二维求解区域划分为若干重叠子域,子域采用有限差分法进行离散并采用LU直接分解法进行独立求解,然后运用Schwarz交替法实现重叠区域解的传递和更新,从而实现大地电磁法二维正演数值模拟.对典型低阻地电模型进行数值模拟实验并与传统全域正演算法相比,表明本文算法的准确性和可行性;同时能够极大节省计算机内存及减小CPU计算时间.另外对重叠区域算法的影响规律研究表明,本文算法所需内存随剖分重叠子域数目增多而降低,CPU计算时间随剖分重叠子域数目增多而先减小后增加;重叠子域组合方式和重叠规模大小对计算效率有一定影响,需进行合理优化.因此本文提出的算法为电磁法三维大规模问题的正反演计算提供了一种新的思路.Domain decomposition algorithm can transform the largescale problems into small problems to solve with reducing computational scale greatly and saving memory space, and has become a powerful means to solve the large-scale complex numerical problems. In this paper, the overlapping domain decomposition method（ Schwarz alternating algorithm） is used for 2-D magnetotelluric（ MT） forward modeling. The model domain is divided into several overlapping sub-domains. Finite difference method is used for discreting sub-domain problems,and LUfactorization is used in solving the problems of sub-domains independently. Then Schwarz alternating algorithm is applied to transmit and update solutions of overlapping domains, so as to realize 2-D MT forward numerical simulation. The typical low resistivity geoelectric model is used for numerical simulation. We compared the results with the traditional algorithm. The comparison results show that the algorithm is accurate and feasible. Memory usage and CPU time of overlapping decomposition method are decreased obviously when compared to the traditional whole domain algorithm. Furthermore, Research shows that memory usage decreases with the increasing of sub-domain number,and CPU time increases first and then decreases with the increasing of sub-domain number. The combination of overlapping sub-domains and solving methods have certain influence on the computational efficiency,which need to be optimized. Therefore,the proposed algorithm provides a new idea for forward and inverse computation of 3-D large-scale problems.

关 键 词：大地电磁法 SCHWARZ交替法 重叠区域分解 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]