An Efficient Cascadic Multigrid Method with Regularization Technique for 3-D Electromagnetic Finite-Element Anisotropic Modelling

Efficient forward modeling of electromagnetic (EM) fields is the basis of interpretation and inversion of the EM data, which plays an important role in practical geophysical exploration. A novel extrapolation cascadic multigird (EXCMG) method is developed to solve large linear systems encountered in geophysical EM modelling. The original curl-curl equation is regularized by including the gradient of a scaled divergence correction term, and linear edge element method is used to discrete the equation. And for the sake of generality, arbitrary anisotropic conductivity is considered.#xD;We propose a novel approach to address the issue of edge unknowns in 3-D edge element discretizations on nonuniform rectilinear grids. Inspired by the original EXCMG method for nodal elements, we introduce a new prolongation operator that treats edge unknowns as defined on the midpoints of edges. This operator aims to provide an accurate approximation of the finite element solution on the refined grid. Utilizing the good initial guess significantly reduces the number of iterations required by the preconditioned BiCGStab, which is employed as smoother for the EXCMG algorithm. Numerical experiments are carried out to validate the accuracy and efficiency of the proposed EXCMG method, including problems with analytical solutions, problems from magnetotellurics (MT) and controlled-source electromagnetic modelling (CSEM). Results indicate that EXCMG is more efficient than traditional Krylov-subspace iterative solvers, the algebraic multigrid solver AGMG and those depend on the auxiliary-space Maxwell solver (AMS), especially for large-scale problems where the number of unknowns exceeds 10 million. The EXCMG method demonstrates good robustness for a wide range of frequencies and complex geo-electric structures.