Comparison the iterative solvers for large sparse matrix in 3D electromagnetic forward modelling

Abstract

In 3D electromagnetic (EM) forward modeling, an analytical solution is generally not available. Numerical solution is commonly applied to solve the forward modeling problems, mostly based on iterative solvers. The efficiency of EM forward modeling is critical for the development of practical inversion for EM data. The Krylov subspace solvers are widely used to solve frequency-domain EM forward modeling problems. However, these solvers converge remarkably more slowly as the operating period increases. This can be improved by the use of preconditioner and divergence correction. Multigrid (MG) solver is efficient for solving EM forward modelling problems without the use of preconditioner and divergence correction. In this paper, a MG solver is compared with Bi-Conjugate Gradients Stabilized (BCG) solvers with different preconditioners. They are compared, in terms of iteration number and computing time, indicating the MG solver is much more efficient.