research-article

Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack

Authors:

Brisa N. Davis,

Randall J. LeVequeAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 46, Issue 3

Article No.: 26, Pages 1 - 28

https://doi.org/10.1145/3392775

Published: 15 September 2020 Publication History

Abstract

Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can selectively refine areas to track discontinuities in the solution. The open source Clawpack software implements block-structured AMR to refine around propagating waves in the AMRClaw package. For problems where the solution must be computed over a large domain but is only of interest in a small area, this approach often refines waves that will not impact the target area. We seek a method that enables the identification and refinement of only the waves that will influence the target area.

Here we show that solving the time-dependent adjoint equation and using a suitable inner product allows for a more precise refinement of the relevant waves. We present the adjoint methodology in general and give details on the implementation of this method in AMRClaw. Examples and a computational performance analysis for linear acoustics equations are presented. The adjoint method is compared to AMR methods already available in AMRClaw, and the advantages and disadvantages are discussed. The approach presented here is implemented in Clawpack, in Version 5.6.1, and code for all examples presented is archived on Github.

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Index Terms

Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 46, Issue 3

September 2020

267 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3410509

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Publication History

Published: 15 September 2020

Online AM: 07 May 2020

Accepted: 01 April 2020

Revised: 01 December 2019

Received: 01 September 2018

Published in TOMS Volume 46, Issue 3

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Cited By

Çatalyürek ÜDevine KFaraj MGottesbüren LHeuer TMeyerhenke HSanders PSchlag SSchulz CSeemaier DWagner D(2023)More Recent Advances in (Hyper)Graph PartitioningACM Computing Surveys10.1145/357180855:12(1-38)Online publication date: 2-Mar-2023
https://dl.acm.org/doi/10.1145/3571808
Yu XLiu X(2023)Evaluation Method of Japanese Teaching Effect Based on Feature Offset CompensationInternational Journal of Computational Intelligence Systems10.1007/s44196-023-00278-716:1Online publication date: 27-Jun-2023
https://doi.org/10.1007/s44196-023-00278-7
Dong Z(2022)Research on Machine Translation Method of English-Chinese Long Sentences Based on Fuzzy Semantic OptimizationMobile Information Systems10.1155/2022/48636232022Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1155/2022/4863623

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