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A High-Order, Conservative Integrator with Local Time-Stepping

Throwe, William and Teukolsky, Saul (2020) A High-Order, Conservative Integrator with Local Time-Stepping. SIAM Journal on Scientific Computing, 42 (6). A3730-A3760. ISSN 1064-8275. https://resolver.caltech.edu/CaltechAUTHORS:20190821-155551404

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Abstract

We present a family of multistep integrators based on the Adams--Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of the system. It can also change with time within a given subdomain. The methods are linearly conservative, preserving a wide class of analytically constant quantities to numerical roundoff, even when numerical truncation error is significantly higher. These methods are intended for use in solving conservative PDEs in discontinuous Galerkin formulations or in finite-difference methods with compact stencils. A numerical test demonstrates these properties and shows that significant speed improvements over the standard Adams--Bashforth schemes can be obtained.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/19M1292692DOIArticle
https://arxiv.org/abs/1811.02499arXivDiscussion Paper
ORCID:
AuthorORCID
Throwe, William0000-0001-5059-4378
Teukolsky, Saul0000-0001-9765-4526
Additional Information:© 2020 Society for Industrial and Applied Mathematics. Submitted to the journal's Methods and Algorithms for Scientific Computing section October 11, 2019; accepted for publication (in revised form) September 21, 2020; published electronically December 1, 2020. This work was partially supported by the Sherman Fairchild Foundation and by NSF through grants PHY-1606654 and ACI-1713678.
Group:Astronomy Department
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFPHY-1606654
NSFACI-1713678
Subject Keywords:local time-stepping, multirate time integration, Adams methods, adaptive time stepping, conservation laws
Issue or Number:6
Classification Code:AMS subject classifications. 65L06, 65L60, 65M20, 65M60, 65Z05
Record Number:CaltechAUTHORS:20190821-155551404
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190821-155551404
Official Citation:A High-Order, Conservative Integrator with Local Time-Stepping. William Throwe and Saul Teukolsky. SIAM Journal on Scientific Computing 2020 42:6, A3730-A3760; DOI: 10.1137/19M1292692
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98091
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Aug 2019 22:59
Last Modified:14 Jan 2021 21:01

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