基于局部加密等级网格的2.5D直流电法有限元模拟  

Finite element modeling of 2.5D DC resistivity based on locally refined graded mesh

作　　者：胡宏伶[1] 肖晓[2] 潘克家[3,4] 汤井田[2] 谢维[2] 

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081 [2]中南大学地球科学与信息物理学院有色金属成矿预测教育部重点实验室,湖南长沙410083 [3]中南大学数学与统计学院,湖南长沙410083 [4]成都理工大学油气藏地质及开发工程国家重点实验室,四川成都610059

出　　处：《中南大学学报（自然科学版）》2014年第7期2259-2267,共9页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(41204082,11301176,41104071);中国博士后科学基金特别资助项目(2013T60781);高等学校博士学科点专项科研基金资助项目(20120162120036);成都理工大学油气藏地质及开发工程国家重点实验室基金资助项目(PLC201305)

摘　　要：合理截取半圆形计算区域,采取局部加密的?-等级网格,结合对称行索引存贮格式(CSR)及并行稀疏直接求解器PARDISO,提出一种高效、高精度的2.5D直流电阻率法有限元正演方案,并编制相应的Fortran程序,对具有解析解的3个典型地电模型进行计算与分析。研究结果表明:圆形截断边界不仅便于在径向方向上采取?-等级网格剖分,而且能大大简化有限元模拟中单元刚度矩阵的计算;结构化的等级网格避开了通常非结构化网格有限元计算时繁琐的网格剖分及总体刚度阵的集成过程,且能在不增大问题规模的前提下,显著提高2.5D直流电法正演源点附近的模拟精度;Intel MKL的PARDISO求解器能在普通PC机上5 s内求解电法正演有限元离散得到的100万阶稀疏线性方程组,可广泛用于各种地球物理正演问题。Truncating semi-circular computational domain reasonably, and combining the compressed sparse row （CSR） format and the parallel direct sparse solver （PARDISO）, an efficient and high-precision finite element method for 2.5D DC resistivity modeling was proposed based on locally refined graded mesh, and the corresponding FORTRAN program was developed. The numerical results and analysis were given for three typical geoelectric models which have analytical solutions. The results show that the circular truncation boundary is not only easy to conduct a l-graded mesh partition in the radial direction, but also can significantly simplify the calculation of the element stiffness matrix in finite element simulations. The structured locally refined graded meshes can not only avoid the cumbersome processes of mesh generation and assembly of global stiffness matrix in finite element computations with usual unstructured meshes, but also significantly improve the accuracy near the source of 2.5D forward modeling of direct current method under the premise of not increasing the size of the problem. The Intel MKL PARDISO solver can solve, a sparse linear system of millions of unknowns arising from finite element discretization of DC modeling on an ordinary PC within 5 s, and can be widely used for a variety of the forward modeling problems in geophysics.

关 键 词：直流电阻率 等级网格 有限元 局部加密 并行稀疏直接求解器 行索引存贮格式 

分 类 号：P631[天文地球—地质矿产勘探]