A review of block Krylov subspace methods for multisource electromagnetic modelling

Practical applications of controlled-source electromagnetic (EM) modelling require solutions for multiple sources at several frequencies, thus leading to a dramatic increase of the computational cost. In this paper, we present an approach using block Krylov subspace solvers that are iterative methods especially designed for problems with multiple right-hand sides (RHS). Their main advantage is the shared subspace for approximate solutions, hence, these methods are expected to converge in less iterations than the corresponding standard solver applied to each linear system. Block solvers also share the same preconditioner, which is constructed only once. Simultaneously computed block operations have better utilization of cache due to the less frequent access to the system matrix. In this paper, we implement two different block solvers for sparse matrices resulting from the finite-difference and the finite-element discretizations, discuss the computational cost of the algorithms and study their dependence on the number of RHS given at once. The effectiveness of the proposed methods is demonstrated on two EM survey scenarios, including a large marine model. As the results of the simulations show, when a powerful preconditioning is employed, block methods are faster than standard iterative techniques in terms of both iterations and time.