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Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge–Kutta Methods

Fekete, Imre LU ; Izsák, Ferenc ; Kupás, Vendel P. and Söderlind, Gustaf LU (2025) In Algorithms 18(8).
Abstract

In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary differential equations. Our focus is particularly on their influence on tolerance proportionality. We examine various grid-refinement strategies within the multigrid reduction-in-time (MGRIT) framework. Our results show that a simple adjustment to the original refinement factor can substantially improve computational stability and reliability. Through numerical experiments on standard test problems using the XBraid library, we demonstrate that parallel-in-time solutions closely match their sequential counterparts. Moreover, with the use of multiple processors,... (More)

In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary differential equations. Our focus is particularly on their influence on tolerance proportionality. We examine various grid-refinement strategies within the multigrid reduction-in-time (MGRIT) framework. Our results show that a simple adjustment to the original refinement factor can substantially improve computational stability and reliability. Through numerical experiments on standard test problems using the XBraid library, we demonstrate that parallel-in-time solutions closely match their sequential counterparts. Moreover, with the use of multiple processors, computing time can be significantly reduced.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
adaptivity, computational stability, high-performance computing, parallel-in-time methods, Runge–Kutta methods, tolerance proportionality
in
Algorithms
volume
18
issue
8
article number
484
publisher
MDPI AG
external identifiers
  • scopus:105014377818
ISSN
1999-4893
DOI
10.3390/a18080484
language
English
LU publication?
yes
id
6f057a3c-6844-43d7-8885-97ca9951b924
date added to LUP
2025-11-07 10:09:22
date last changed
2025-11-07 10:09:57
@article{6f057a3c-6844-43d7-8885-97ca9951b924,
  abstract     = {{<p>In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary differential equations. Our focus is particularly on their influence on tolerance proportionality. We examine various grid-refinement strategies within the multigrid reduction-in-time (MGRIT) framework. Our results show that a simple adjustment to the original refinement factor can substantially improve computational stability and reliability. Through numerical experiments on standard test problems using the XBraid library, we demonstrate that parallel-in-time solutions closely match their sequential counterparts. Moreover, with the use of multiple processors, computing time can be significantly reduced.</p>}},
  author       = {{Fekete, Imre and Izsák, Ferenc and Kupás, Vendel P. and Söderlind, Gustaf}},
  issn         = {{1999-4893}},
  keywords     = {{adaptivity; computational stability; high-performance computing; parallel-in-time methods; Runge–Kutta methods; tolerance proportionality}},
  language     = {{eng}},
  number       = {{8}},
  publisher    = {{MDPI AG}},
  series       = {{Algorithms}},
  title        = {{Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge–Kutta Methods}},
  url          = {{http://dx.doi.org/10.3390/a18080484}},
  doi          = {{10.3390/a18080484}},
  volume       = {{18}},
  year         = {{2025}},
}