Fast 3D magnetotelluric modelling using Yee's scheme and extrapolation multigrid solver

Fast magnetotelluric (MT) forward modelling is the core engine of interpreting and inversion of MT data. However, traditional iterative or multigrid solvers may converge slow or diverge when solving large-scale forward problems. Hence, we develop an extrapolation cascadic multigrid (EXCMG) solver on structured rectilinear grid to accelerate the solution of large linear systems arising from the finite difference discretization of the Maxwell's equations. General anisotropic conductivity is considered. Staggered Yee's grid is employed, and a new prolongation operator based on global extrapolation and quartic interpolation to tackle the issue caused by non-nested unknowns' distribution. Several examples are tested to validate the accuracy and efficiency of the proposed algorithm, including a layered-earth model, a three-block model and the Cascadia model from real-world. Results show that our EXCMG solver is far more efficient than traditional iterative solver, e.g., BiCGStab, as well as some geometric multigrid (GMG) methods, e.g., the one developed by Guo et al. (2022).