On the Minimal Shift in the Shifted Laplacian Preconditioner for Multigrid to Work

DOI10.1007/978-3-319-18827-0_12zbMath1339.65231OpenAlexW2464766188MaRDI QIDQ2814990

Martin J. Gander, Pierre-Henri Cocquet

Publication date: 23 June 2016

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-18827-0_12

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Preconditioners for iterative methods (65F08)

Related Items (6)

A coercive heterogeneous media Helmholtz model: formulation, wavenumber-explicit analysis, and preconditioned high-order FEM ⋮ Analysis of the Shifted Helmholtz Expansion Preconditioner for the Helmholtz Equation ⋮ Restrictions on the Use of Sweeping Type Preconditioners for Helmholtz Problems ⋮ How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid? ⋮ On block triangular preconditioned iteration methods for solving the Helmholtz equation ⋮ Closed Form Dispersion Corrections Including a Real Shifted WaveNumber for Finite Difference Discretizations of 2D Constant Coefficient Helmholtz Problems

Cites Work

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• An iterative method for the Helmholtz equation
• Advances in iterative methods and preconditioners for the Helmholtz equation
• On a class of preconditioners for solving the Helmholtz equation
• An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Local Fourier analysis of the complex shifted Laplacian preconditioner for Helmholtz problems
• Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
• Multigrid methods for Helmholtz problems: A convergent scheme in 1D using standard components

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