GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Second-order absorbing boundary conditions for the wave equation: a solution for the corner problem
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Factorizing complex symmetric matrices with positive definite real and imaginary parts
Mathematics of Computation
Separation-of-variables as a preconditioner for an iterative Helmholtz solver
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Applied Numerical Mathematics
A fast iterative solver for scattering by elastic objects in layered media
Applied Numerical Mathematics
Controllability method for acoustic scattering with spectral elements
Journal of Computational and Applied Mathematics
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Journal of Computational Physics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
The efficient solution of electromagnetic scattering for inhomogeneous media
Journal of Computational and Applied Mathematics
Preconditioning techniques for the iterative solution of scattering problems
Journal of Computational and Applied Mathematics
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Acoustic inverse scattering via Helmholtz operator factorization and optimization
Journal of Computational Physics
Equation-based interpolation and incremental unknowns for solving the Helmholtz equation
Applied Numerical Mathematics
The Iterative Solver RISOLV with Application to the Exterior Helmholtz Problem
SIAM Journal on Scientific Computing
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method
Journal of Computational and Applied Mathematics
A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements
Journal of Computational Physics
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity
Journal of Scientific Computing
A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation
Journal of Computational Physics
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In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called "shifted Laplace" preconditioners of the form Δφ-αk2φ with α ∈ C. Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.