Removing numerical dispersion from linear evolution equations
Numerical Analysis
2021-09-15 v3 Numerical Analysis
Computational Physics
Geophysics
Abstract
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized as certain Fourier integral operators, called time dispersion transforms, and we prove that, under an assumption about the frequency content, it yields a solution with correct evolution throughout the entire lifespan. We demonstrate the method on a model equation as well as on the simulation of elastic and viscoelastic wave propagation.
Cite
@article{arxiv.1906.10743,
title = {Removing numerical dispersion from linear evolution equations},
author = {Jens Wittsten and Erik F. M. Koene and Fredrik Andersson and Johan O. A. Robertsson},
journal= {arXiv preprint arXiv:1906.10743},
year = {2021}
}
Comments
41 pages, 8 figures