## Positive stable preconditioners for symmetric indefinite linear systems arising from Helmholtz equations.(English)Zbl 1231.78010

Summary: Using the finite difference method to discretize Helmholtz equations usually leads to a large spare linear system of equations $$Ax=b$$. Since the coefficient matrix $$A$$ is frequently indefinite, it is difficult to solve iteratively. The approach taken in this Letter is to precondition this linear system with positive stable preconditioners and then to solve it iteratively using Krylov subspace methods. Numerical experiments are given in order to demonstrate the efficiency of the presented preconditioners.

### MSC:

 78A25 Electromagnetic theory (general) 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 65F10 Iterative numerical methods for linear systems
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