基于区域分解和混合有限元的大地电磁三维并行正反演研究

项目名称： 基于区域分解和混合有限元的大地电磁三维并行正反演研究

项目编号： No.41464002

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 李长伟

作者单位： 桂林理工大学

项目金额： 45万元

中文摘要： 三维电磁场响应的复杂性和反问题的不适定特性造成了三维大地电磁正反演的复杂性，而问题规模和数据量巨增造成的速度和存储问题是制约三维正反演实用性的关键因素。本项目拟采用混合有限元形式解决复杂地质结构的三维正演问题，根据正则化思想引入解空间约束，利用不精确的高斯-牛顿算法进行三维反演求解。在正演模拟中，用非结构化网格剖分的矢量有限元离散电场矢量，同时采用Lagrange乘子法，在2阶双旋度微分方程基础上施加电荷守恒限制条件，去除双旋度算子零空间，避免低频模拟时的伪解。在正反演框架中，引入分而治之的并行计算策略，分割区域为多个非交错子域，相邻子域间通过边界匹配条件耦合，把计算任务按子域分解做粗粒度并行。项目拟基于相关研究，克服低频电磁场模拟求解的困难，解决三维正反演中速度和存储的瓶颈问题，形成一套适合起伏地形等复杂地质条件下正反演并行化理论和算法体系，提高三维大地电磁正反演的应用水平。

中文关键词： 大地电磁；正反演；并行计算；区域分解；混合有限元

英文摘要： The practical three-dimension forward modeling and inversion of magnetotelluric method still remain challenging today.In addition to the complexity of electromagnetic responses on topography and complicated medium and the ill-poseness of the inverse problems, the large computational cost in terms of both memory and CPU time is a critical obstructive factor in its realistic application. In this project we will solve the forward problem using an mixed finite element method, regularization and the inexact Gauss-Newton method are used to obtain reasonable solution of inverse problem.Based on the second-order curl-curl equation, vectorial finite element discretization on an unstructured grid is applied for the approximation of the vector field, and the divergence-free condition is enforced by Lagrange multiplier to eliminate spurious solutions by removing the null space of the curl-curl operator.In this forward and inverse framework we present a divide and conquer methods to implement coarse grain parallel computing. It splits a global computational domain into many smaller non-overlapping subdomains and divide the computational tasks by subdomains.The local problems in neighborhood domains are coupled with matching condition onto the boundaries.The goal of this project is to address the difficulty for solving low frequency problems, overcome the speed and memory bottleneck, build up a parallel theoretical and algorithmic system for forward and inverse problem with complicated geological structure and topography,and improve the level of practical application for MT 3D forward modeling and inversion.

英文关键词： magnetotelluric;modeling and inversion;parallel computing;domain decomposition;mixed finite element