A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

DOI10.1016/j.jcp.2018.03.046zbMath1398.65268OpenAlexW2796152264MaRDI QIDQ1783444

Tariq Alkhalifah, Zedong Wu

Publication date: 20 September 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10754/627484

zbMATH Keywords

finite differenceacoustic wave equationdispersion erroranisotropic

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 (11)

Time-space domain dispersion reduction schemes in the uniform norm for the 2D acoustic wave equation ⋮ An efficient high-order compact finite difference method for the Helmholtz equation ⋮ 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 study of exterior acoustic problems using a novel finite element-least square point interpolation method with perfectly matched layer ⋮ Fast Poynting-vector based wave-mode separation and RTM in 2D elastic TI media ⋮ Numerical solutions for the Helmholtz boundary value problems of anisotropic homogeneous media ⋮ Unnamed Item ⋮ A new finite difference scheme for the 3D Helmholtz equation with a preconditioned iterative solver ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes ⋮ Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions

Uses Software

• MUMPS
• STRUMPACK

Cites Work

• Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions
• A compact fourth order scheme for the Helmholtz equation in polar coordinates
• Accurate finite difference methods for time-harmonic wave propagation
• The method of difference potentials for the Helmholtz equation using compact high order schemes
• High-order finite difference methods for the Helmholtz equation
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling
• A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
• Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

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