An efficient spectral element method for two-dimensional magnetotelluric modeling - Tong, Xiaozhong; Sun, Ya; Zhang, Boyao (Frontiers in Earth Science, 2023)
We introduce a new efficient spectral-element approach to solve the two-dimensional magnetotelluric forward problem based on Gauss-Lobatto-Legendre polynomials. It can combine the high-accuracy of the spectral technique and perfect flexibility of the finite-element approach, which can significantly improve the smoothness and calculation accuracy. This method mainly includes two steps: (1) transformation of the boundary value problem in partial differential form into the variational problem in integral form and (2) solving large symmetric sparse systems based on the combination of an incomplete LU factorization and the double conjugate gradient stability algorithm through the spectral element with quadrilateral meshes. We imply the spectral-element method on a resistivity half-space model to obtain a simple analytical solution and find that the magnetic field solutions simulated by the spectral-element approach are highly matched with the exact solutions. The experiment shows that the spectral-element solution has high accuracy with coarse meshes. We further compare the numerical results of the spectral-element, finite-difference, and finite-element approaches calculated on the COMMEMI 2D-1 and smooth models, respectively. The numerical results of the spectral-element procedure are highly consistent with the other two techniques. All numerical results indicate that the spectral-element method can be efficient method for solving magnetotelluric forward problem, which can get accurate numerical results with less sensitivity to mesh quality than the finite-element algorithm. To expand the application of the spectral-element process, future work will test the performance of this spectral-element approach on three-dimensional structures.