基于Schwarz重叠型区域分解的大地电磁二维正演研究

发布时间：2019-01-05 09:53

【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.
[Abstract]:Domain decomposition algorithm has become a powerful method to solve large scale complex numerical problems by transforming large scale problems into some small problems and greatly reducing the scale of computation and saving memory space. In this paper, the (MT) two-dimensional forward modeling of magnetotelluric method is taken as an example, the two-dimensional solution region is divided into several overlapping subdomains, the subdomains are discretized by the finite difference method and the LU direct decomposition method is used to solve them independently. Then the Schwarz alternating method is used to transfer and update the solution of overlapped region, thus the two-dimensional forward numerical simulation of magnetotelluric method is realized. Numerical simulation experiments on typical low-resistivity geoelectric models show that the proposed algorithm is accurate and feasible compared with the traditional global forward algorithm, and can greatly save computer memory and reduce CPU computing time. In addition, the study on the effect of overlapping region algorithm shows that the memory required by this algorithm decreases with the number of overlapping subfields, and the CPU computing time decreases first and then increases with the number of overlapping subfields. The combination of overlapping subdomains and the size of overlapped subdomains have a certain effect on the calculation efficiency, which need to be optimized reasonably. Therefore, the algorithm presented in this paper provides a new idea for the forward inversion of electromagnetic method for three dimensional large scale problems.
【作者单位】：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;
【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
【分类号】：P631.325

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