GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Crout Versions of ILU for General Sparse Matrices
SIAM Journal on Scientific Computing
Using the parallel algebraic recursive multilevel solver in modern physical applications
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
Multilevel ILU With Reorderings for Diagonal Dominance
SIAM Journal on Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
SIAM Journal on Scientific Computing
Greedy Coarsening Strategies for Nonsymmetric Problems
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
Modification and Compensation Strategies for Threshold-based Incomplete Factorizations
SIAM Journal on Scientific Computing
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity
Journal of Scientific Computing
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Linear systems which originate from the simulation of wave propagation phenomena can be very difficult to solve by iterative methods. These systems are typically complex valued and they tend to be highly indefinite, which renders the standard ILU-based preconditioners ineffective. This paper presents a study of ways to enhance standard preconditioners by altering the diagonal by imaginary shifts. Prior work indicates that modifying the diagonal entries during the incomplete factorization process, by adding to it purely imaginary values can improve the quality of the preconditioner in a substantial way. Here we propose simple algebraic heuristics to perform the shifting and test these techniques with the ARMS and ILUT preconditioners. Comparisons are made with applications stemming from the diffraction of an acoustic wave incident on a bounded obstacle (governed by the Helmholtz Wave Equation).