Stability of Structure-Aware Taylor Methods for Tents

Authors

Jay Gopalakrishnan, Portland State UniversityFollow
Zheng Sun, University of Alabama - Tuscaloosa

Sponsor

NSF grant DMS-1912779, NSF grant DMS-2208391

Published In

Mathematics of Computation

Document Type

Post-Print

Publication Date

2023

Abstract

Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are useful to design explicit time marching schemes on unstructured advancing fronts with built-in locally variable timestepping for arbitrary spatial and temporal discretization orders. The main result of this paper is that an s-stage SAT timestepping within a tent is weakly stable under the time step constraint

∆t ≤ Ch^1+1/s , where ∆t is the time step size and h is the spatial mesh size. Improved stability properties are also presented for high-order SAT time discretizations coupled with low-order spatial polynomials. A numerical verification of the sharpness of proven estimates is also included.

Rights

This work is licensed under a Creative Commons Attribution 4.0 International License.

Description

First published in Mathematics of Computation in 92 2023, published by the American Mathematical Society

Locate the Document

https://doi.org/10.1090/mcom/3811

DOI

10.1090/mcom/3811

Persistent Identifier

https://archives.pdx.edu/ds/psu/39562

Citation Details

Gopalakrishnan, Jay and Sun, Zheng, "Stability of Structure-Aware Taylor Methods for Tents" (2023). Mathematics and Statistics Faculty Publications and Presentations. 364.
https://archives.pdx.edu/ds/psu/39562