Algebraic multigrid preconditioning for finite-element methods for 3-D electromagnetic modelling in geophysics

Abstract

Efficiency of a 3-D electromagnetic numerical modelling scheme is critical for its future use within a 3-D electromagnetic inversion algorithm. Therefore, we have developed and implemented a more elaborate preconditioning technique for Krylov subspace methods to improve the performance and reduce the execution time of nodal finite-element solvers for 3-D electromagnetic modelling in geophysics. This new preconditioner is based on algebraic multigrid that uses different basic relaxation methods as smoothers, such as Jacobi, Gauss-Seidel and symmetric successive over-relaxation, and the wave-front algorithm to create groups, on which generation of coarse spaces is based. Also, it is designed as a black box, so that it can be employed by different iterative methods without any additional modifications of the solver's algorithm. Tests for various problems with different conductivity structures and characteristics have shown that our preconditioner improves the convergence of different iterative solvers to a great extent and thus significantly reduces the total execution time of the whole program.