Solution Strategies for Complex 2D/3D Magnetotelluric Forward Modeling Based on the Finite Element Method
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摘要: 复杂二维和三维大地电磁模型的正演数值模拟具有一定的挑战性。对于复杂的二维和三维大地电磁正演问题,我们采用有限单元法进行求解。有限单元法最后形成一个线性方程组,系数矩阵是大型稀疏的带状对称复系数矩阵,并且其条件数远大于1,为严重病态矩阵,求解其对应方程组会遇到很多困难。不完全LU分解处理的Bi-CGSTAB迭代方法可用于该线性方程组的求解,并且具有速度快、精度高和稳定性好等优点;为了模拟无穷远边界及满足计算机的内存需求,在保证计算精度的情况下设计了非均匀网格剖分;在程序编制中,只存储有限元系数矩阵的非零元素,大大减少了正演计算的时间。通过对二维和三维模型电磁响应的计算,验证了算法的正确性。
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关键词:
- 大地电磁 /
- 有限单元法 /
- 正演模拟 /
- Bi-CGSTAB算法
Abstract: Two-dimensional(2D) or three-dimensional(3D) forward modeling is a challenge for geometrically complex magnetotelluric(MT) problems.To solve the complex 2D/3D MT forward problems,we apply the finite element method.The finite element method is used to form a linear equation,and the coefficient matrix is a large sparse,banded,symmetric,conditioned,complex matrix.Its condition number is far larger than 1,and it is an ill-conditioned matrix.Solving large scale ill-conditioned linear equation is very difficult.The Bi-CGSTAB algorithm with incomplete LU decomposition for preconditioning could be used to solve this system linear equation,with advantages of high speed,high precision and stability;In order to simulate the infinity border and meet the demand computer memory,the non-uniform gird is designed with ensuring the accuracy;In programming,we only store the non-zero elements of the finite element matrix.By numerical simulation of 2D/3D MT responses,we verified the correctness of the magnetotelluric forward method.-
Keywords:
- magnetotelluric /
- forward modeling /
- finite element method /
- Bi-CGSTAB algorithm
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