Analysis of the Shifted Helmholtz Expansion Preconditioner for the Helmholtz Equation

DOI10.1007/978-3-319-93873-8_17zbMath1443.65321OpenAlexW2906845668MaRDI QIDQ5114537

Pierre-Henri Cocquet, Martin J. Gander

Publication date: 24 June 2020

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

Full work available at URL: https://doi.org/10.1007/978-3-319-93873-8_17

zbMATH Keywords

finite elementsGMRESHelmholtz equationpreconditioner

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Preconditioners for iterative methods (65F08)

Related Items (2)

Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? ⋮ Closed Form Dispersion Corrections Including a Real Shifted WaveNumber for Finite Difference Discretizations of 2D Constant Coefficient Helmholtz Problems

Cites Work

• Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
• On a class of preconditioners for solving the Helmholtz equation
• On the Minimal Shift in the Shifted Laplacian Preconditioner for Multigrid to Work
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
• Domain Decomposition Algorithms for Indefinite Elliptic Problems
• Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
• On the Optimality of Shifted Laplacian in a Class of Polynomial Preconditioners for the Helmholtz Equation
• How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid?

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