Efficient Solution Scheme for Large-Scale Anisotropic Forward Modeling of 3-D Magnetotelluric Data

Efficient 3-D magnetotelluric anisotropy forward modeling is one of the key research techniques used for inversion interpretation. We propose an improved multi-level down-sampling scheme (IMLDS) to reduce the degrees of freedom of the stiffness matrix derived from the edge-based finite element method to improve the computational efficiency, saving on memory usage and calculation time for the forward modeling. Then, to further reduce the memory requirements and speed up the solution of the discretized electric system, we develop a multiple right-hand direct–iterative hybrid solver (MDIHS) based on a block rational Krylov preconditioner. The solver we propose can further save computational costs and time based on the IMLDS. Moreover, the convergence performance of the direct–iterative solver is less affected by the frequency, which solves the problem of slow convergence of the electric field control equation at low frequencies. We also use the high-level language Julia, which is easy to load into third-party packages, to ensure the stability and efficiency of the program. Finally, the validity and advantages of the two schemes are analyzed in detail using three examples. The examples’ results show that the MDIHS and improved multi-level down-sampling can significantly reduce computational memory and save computational time.