Algebraic Multigrid Preconditioning in Parallel Finite-element Solvers

This work presents an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based ¿nite-element solvers for three-dimensional electromagnetic numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid that uses di¿erent basic relaxation methods, such as Jacobi, symmetric successive over-relaxation and Gauss-Seidel, as smoothers and the wave-front algorithm to create groups, which are used for coarse-level generation. The preconditioner has been implemented and tested within a parallel nodal ¿nite-element solver for three-dimensional forward problems in electromagnetic induction geophysics. A series of experiments for several models with di¿erent conductivity structures and characteristics have been performed to test the performance of the algebraic multigrid preconditioning technique when combined with biconjugate gradient stabilised method. The results have shown that the preconditioner greatly improves the convergence of the iterative solver and reduces the total execution time of the forward-problem code.