Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations

Owe Axelsson (1) , János Karátson (2) , Frédéric Magoulès (3, 4)

1 AS CR - Institute of Systems Biology and Ecology
2 ELTE - Eötvös Loránd University
3 CentraleSupélec
4 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

Complex-valued Helmholtz equations arise in various applications, and a lot of research has been devoted to finding efficient preconditioners for the iterative solution of their discretizations. In this paper we consider the Helmholtz equation rewritten in real-valued block form, and use a preconditioner in a special two-by-two block form. We show that the corresponding preconditioned Krylov iteration converges at a mesh-independent superlinear rate.

Keywords: Helmholtz equations; Iterative solution; Preconditioning; Mesh-independent superlinear convergence

Domains: Numerical Analysis [math.NA]

Owe Axelsson, János Karátson, Frédéric Magoulès. Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations. Journal of Computational and Applied Mathematics, 2018, 340, pp.424-431. ⟨10.1016/j.cam.2018.01.029⟩. ⟨hal-01708720⟩