This paper addresses the problem of efficient solution of large sparse linear systems arising in 3D finite-element (FE) electromagnetic modeling on structured hexahedral grids. Preconditioned iterative solvers are known to be both memory and time efficient given an appropriate preconditioner is provided. To design such a preconditioner, we exploit the relation between finite-element and finite-difference (FD) matrices. We first considered a preconditioner based on the FD matrix that corresponds to a layered earth. This matrix has been used to precondition FD systems in the past. For FE systems, however, it did not provide convergence of an iterative solver whenever hexahedrons are deformed. To gain robustness, we combined the FD preconditioner with a smoothing procedure. This type of preconditioning has not been published earlier. The obtained preconditioner happens to be fast, robust, and applicable to realistic electromagnetic modeling. We demonstrated effectiveness of this approach on a real model from the Black Sea continental slope.


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