An optimal 25-point finite difference scheme for the Helmholtz equation with PML

DOI10.1016/j.cam.2011.08.007zbMath1233.65076OpenAlexW1966763308MaRDI QIDQ654737

Zhongying Chen, Tingting Wu, Hong-qi Yang

Publication date: 21 December 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.08.007

zbMATH Keywords

numerical experimentsHelmholtz equationperfectly matched layernumerical dispersion25-point finite difference scheme

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 (14)

A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer ⋮ A dispersion minimizing finite difference scheme for the Helmholtz equation based on point-weighting ⋮ A dispersion minimizing subgridding finite difference scheme for the Helmholtz equation with PML ⋮ CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR ⋮ High-order compact finite difference methods for solving the high-dimensional Helmholtz equations ⋮ Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect ⋮ Nine-point compact sixth-order approximation for two-dimensional nonlinear elliptic partial differential equations: application to bi- and tri-harmonic boundary value problems ⋮ A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation ⋮ A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme ⋮ Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients ⋮ Adaptive finite element method for the sound wave problems in two kinds of media ⋮ Optimal 25-point finite-difference subgridding techniques for the 2D Helmholtz equation ⋮ A dispersion minimizing compact finite difference scheme for the 2D Helmholtz equation ⋮ An optimal fourth-order finite difference scheme for the Helmholtz equation based on the technique of matched interface boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mixed unsplit-field perfectly matched layers for transient simulations of scalar waves in heterogeneous domains
• The inverse medium problem in heterogeneous PML-truncated domains using scalar probing waves
• A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
• Absorbing PML boundary layers for wave-like equations
• A perfectly matched layer for the absorption of electromagnetic waves
• 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
• High-order finite difference methods for the Helmholtz equation
• A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• Group Velocity in Finite Difference Schemes
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• 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
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

This page was built for publication: An optimal 25-point finite difference scheme for the Helmholtz equation with PML