Closed Form Dispersion Corrections Including a Real Shifted WaveNumber for Finite Difference Discretizations of 2D Constant Coefficient Helmholtz Problems

DOI10.1137/19M1304350zbMath1464.35064MaRDI QIDQ5857838

Pierre-Henri Cocquet, Xueshuang Xiang, Martin J. Gander

Publication date: 8 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

finite difference methodHelmholtz equationnumerical dispersionrectangular domainsconstant wavenumbers

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (6)

Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D ⋮ Conditioning analysis for discrete Helmholtz problems ⋮ A semi matrix-free twogrid preconditioner for the Helmholtz equation with near optimal shifts ⋮ Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect ⋮ Asymptotic Dispersion Correction in General Finite Difference Schemes for Helmholtz Problems ⋮ Pollution and accuracy of solutions of the Helmholtz equation: a novel perspective from the eigenvalues

Cites Work

• Unnamed Item
• Unnamed Item
• Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed?
• A dispersion minimizing compact finite difference scheme for the 2D Helmholtz equation
• Compact finite difference schemes of sixth order for the Helmholtz equation
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• An optimal compact sixth-order finite difference scheme for the Helmholtz equation
• Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?
• Accurate finite difference methods for time-harmonic wave propagation
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• Dispersion correction for Helmholtz in 1D with piecewise constant wavenumber
• A coercive heterogeneous media Helmholtz model: formulation, wavenumber-explicit analysis, and preconditioned high-order FEM
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
• A dispersion minimizing finite difference scheme for the Helmholtz equation based on point-weighting
• A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation
• Contributions to the mathematics of the nonstandard finite difference method and applications
• On the Minimal Shift in the Shifted Laplacian Preconditioner for Multigrid to Work
• Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
• A fourth-order compact scheme for the Helmholtz equation: Alpha-interpolation of FEM and FDM stencils
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
• On Multigrid Convergence in the Indefinite Case
• Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
• Analysis of the Shifted Helmholtz Expansion Preconditioner for the Helmholtz Equation
• A Finite Difference Method with Optimized Dispersion Correction for the Helmholtz Equation
• Is the Helmholtz Equation Really Sign-Indefinite?
• A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections
• Multigrid methods for Helmholtz problems: A convergent scheme in 1D using standard components
• How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid?

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