Comparison of iterative and direct solvers for 3D CSEM modeling

Abstract

Electromagnetic (EM) modeling in frequency domain requires solving large linear systems of equations. This can be accomplished using direct or iterative techniques. We compare the performance of the direct MUMPS and an iterative QMR solver for controlled-source EM modeling on distributed computing platforms. We first establish a conductivity value for air that lets the iterative solver converge while maintaining accuracy of subsurface EM fields, and then demonstrate the accuracy of the direct and iterative solutions. We consider the influence of model size, the number of right hand sides, parallelization approaches, and hardware architecture on performance. Clearly, iterative solutions are significantly more efficient than direct ones for small numbers of right hand sides. Nevertheless, we find that for simulations of moderatesized models on a modern, moderate-sized cluster, the point at which iterative solver runtime exceeds that of the direct solver is reached for relatively small numbers of right hand sides.