Vol. 3, No. 2, 2021
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Removing numerical dispersion from linear evolution equations

Jens Wittsten, Erik F. M. Koene, Fredrik Andersson and Johan O. A. Robertsson
Vol. 3 (2021), No. 2, 253–293
DOI: 10.2140/paa.2021.3.253
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.

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Keywords
evolution equation, finite difference operator, numerical dispersion, time dispersion transform, wave propagation
Mathematical Subject Classification 2010
Primary: 65M06
Secondary: 35A22, 35Q86, 35S30
Milestones
Received: 30 October 2019
Revised: 13 December 2020
Accepted: 19 January 2021
Published: 31 July 2021
Authors
Jens Wittsten
Centre for Mathematical Sciences
Lund University
Sweden		 Department of Engineering
University of Borås
Borås
Sweden
Erik F. M. Koene
Institute of Geophysics
ETH Zürich
Zürich
Switzerland
Fredrik Andersson
Institute of Geophysics
ETH Zürich
Zürich
Switzerland
Johan O. A. Robertsson
Institute of Geophysics
ETH Zürich
Zürich
Switzerland