Work

Fourier beyond dispersion: Wavenumber explicit and precise accuracy of FDMs for the Helmholtz equation

Year: 2025

Type: article

Abstract: We propose a practical tool for evaluating and comparing the accuracy of FDMs for the Helmholtz equation. The tool based on Fourier analysis makes it easy to find wavenumber explicit order of convergence, and can be used for rigorous proof. It fills in the gap between the dispersion analysis and the actual error with source term. We illustrate it for classical and some dispersion free schemes in 1D, with conclusions verified by numerical experiments.

Source: Applied Mathematics Letters

DOI: 10.1016/j.aml.2025.109576

Author: Hui Zhang

Institution: Xi’an Jiaotong-Liverpool University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,800

OpenAlex ID: W4409453420

FWCI: 0.891

Cites: 16

Cited by: 2

Related to: 10