Two-dimensional magnetotelluric anisotropic finite element modeling with undulating terrains based on unstructured extrapolation multigrid method
PAN Kejia1, HAN Xu1, WANG Pengde1, WANG Jinxuan1, XIAO Xiao2, ZHANG Lincheng3
1. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China; 2. School of Geosciences and Info-Physics, Central South University, Changsha, Hunan 410083, China; 3. School of Information and Electronic Engineering, Hunan City University, Yiyang, Hunan 413002, China
Abstract：Magnetotelluric anisotropic finite element forward modeling based on unstructured grids has a slow convergence rate if the classical iterative method is used, and it is not suitable for the forward calculation of complex geoelectric models. The multigrid method, as an improvement to the classical iterative method, is an effective algorithm for solving discrete linear systems of elliptic equations. However, the classical multigrid method relies on nested orthogonal grids and cannot be directly applied to solve unstructured grid problems. Therefore, the authors propose the concept of semi-structured grids. In other words, an initial unstructured grid receives binary encryption level by level, and an extrapolation cascadic multigrid method (EXCMG) is used to quickly solve the large-scale complex linear system derived from two-dimensional magnetotelluric finite element forward modeling in anisotropic media. The EXCMG uses extrapolation and high-order interpolation techniques on a triangular grid to construct a new multigrid prolongation operator and construct the high-order approximation to the finite element solution on refined grids with numerical solutions on two coarse meshes, which is then used as the iterative initial value of the multigrid smoothing operator, namely, BiCGStab, so as to accelerate its convergence. The method is tested with international standard test models (COMMEMI-2D1 and COMMEMI-2D4), and the relative differences of the apparent resistivity and phase are within 1%. In addition, the solution time of the method is significantly reduced compared with that of BiCGStab and aggregation algebraic multigrid method (AGMG). The EXCMG shows excellent scalability and adaptability and can handle complex geoelectric models, arbitrary undulating terrains, and anisotropic problems.
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