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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。
Forward modeling of complex two-dimensional and three-dimensional geomagnetic models has some challenges. For complex two-dimensional and three-dimensional geomagnetic forward problems, we use the finite element method to solve. The finite element method finally forms a linear system of equations. The coefficient matrix is a large and sparse strip symmetric complex coefficient matrix, and its condition number is far greater than 1, which is a serious ill-posed matrix. Many difficulties will be encountered when solving the corresponding equations. The Bi-CGSTAB iterative method with incomplete LU decomposition can be used to solve the linear system of equations, and has the advantages of fast speed, high precision and good stability. In order to simulate the infinity boundary and meet the memory requirements of the computer, In the programming, only the non-zero element of the finite element coefficient matrix is stored, which greatly reduces the time of forward calculation. The correctness of the algorithm is verified by calculating the electromagnetic response of 2D and 3D models.