A dispersion minimizing finite difference scheme for the Helmholtz equation based on point-weighting

DOI10.1016/j.camwa.2017.04.005zbMath1373.65077OpenAlexW2609596110MaRDI QIDQ2403840

Dongsheng Cheng, Xu Tan, Taishan Zeng

Publication date: 12 September 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.04.005

zbMATH Keywords

convergencenumerical examplefinite difference schemeHelmholtz equationperfectly matched layernumerical dispersion

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (14)

An optimized finite element method for the analysis of 3D acoustic cavities with impedance boundary conditions ⋮ CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR ⋮ Numerical analysis of the optimal 9-point finite difference scheme for the Helmholtz equation ⋮ High-order compact finite difference methods for solving the high-dimensional Helmholtz equations ⋮ Asymptotic Dispersion Correction in General Finite Difference Schemes for Helmholtz Problems ⋮ A Finite Difference Method with Optimized Dispersion Correction for the Helmholtz Equation ⋮ A fourth-order optimal finite difference scheme for the Helmholtz equation with PML ⋮ An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition ⋮ An optimal compact sixth-order finite difference scheme for the Helmholtz equation ⋮ A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition ⋮ A robust optimal finite difference scheme for the three-dimensional Helmholtz equation ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes ⋮ An optimal fourth-order finite difference scheme for the Helmholtz equation based on the technique of matched interface boundary ⋮ Closed Form Dispersion Corrections Including a Real Shifted WaveNumber for Finite Difference Discretizations of 2D Constant Coefficient Helmholtz Problems

Cites Work

• Unnamed Item
• Unnamed Item
• A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation
• Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions
• A dispersion minimizing subgridding finite difference scheme for the Helmholtz equation with PML
• An optimal 25-point finite difference scheme for the Helmholtz equation with PML
• A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
• Compact finite difference schemes of sixth order for the Helmholtz equation
• A perfectly matched layer for the absorption of electromagnetic waves
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
• A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation
• SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION
• ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
• An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures
• Group Velocity in Finite Difference Schemes
• Absorbing boundary conditions for electromagnetic wave propagation
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
• Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
• GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE

This page was built for publication: A dispersion minimizing finite difference scheme for the Helmholtz equation based on point-weighting