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Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge–Kutta Methods
Title / Series / Name
Algorithms
Publication Volume
18
Publication Issue
8
Pages
Editors
Keywords
Runge–Kutta methods
adaptivity
computational stability
high-performance computing
parallel-in-time methods
tolerance proportionality
Theoretical Computer Science
Numerical Analysis
Computational Theory and Mathematics
Computational Mathematics
adaptivity
computational stability
high-performance computing
parallel-in-time methods
tolerance proportionality
Theoretical Computer Science
Numerical Analysis
Computational Theory and Mathematics
Computational Mathematics
Files
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Fekete-Imre2_2025.pdf
Adobe PDF, 833.12 KB
URI
https://hdl.handle.net/20.500.14018/27881
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, computing time can be significantly reduced.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2025-08-05
Language
ISBN
Identifiers
10.3390/a18080484