A comparative analysis of Krylov Solvers for three-dimensional simulations of borehole sensors

Abstract

We perform a comparative analysis of three Krylov subspace methods, viz., the restarted generalized minimum residual (RGMRES), the conjugate gradient squared (CGS), and the stabilized biconjugate gradient (Bi-CGSTAB), for solving large non-Hermitian sparse linear systems arising from the 3-D finite-volume modeling of electromagnetic borehole sensors in complex earth formations. Incomplete LU factorization and symmetric successive overrelaxation preconditioning strategies are used to speed up the convergence rate. We compare these algorithms in terms of accuracy, convergence rate, and overall CPU time. Results show that CGS has a highly irregular convergence behavior, whereas RGMRES and Bi-CGSTAB provide similar numerical accuracy. However, the convergence rate and CPU time of the latter depend on the borehole sensor geometry and on the type of preconditioner adopted.