Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 1 h ago
PreprintCC BY 4.0arXiv

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

  • Imre Fekete
  • Ferenc Izsák
  • Vendel P. Kupás
  • Gustaf Söderlind
Open at sourcePDFDOICite

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.

Versions

Related

  1. A Parallel Adaptive Proximal ADMM for Linearly Constrained Separable Composite Optimization Problems
    Leandro F. Maia, Renato D. C. Monteiro, Gilson N. Silva
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  2. Serial Depth of Adaptive Parallel Sampling: Lower Bounds and Schedules for Masked Diffusion Models
    Chuling Wen, Weijie Liang, Jian Lu +1
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Statistical-computational trade-offs for recursive adaptive partitioning estimators
    Yan Shuo Tan, Jason M. Klusowski, Krishnakumar Balasubramanian
    The Annals of StatisticsPeer-reviewedLicence not statedFull text10 citedStatisticsOpenAlex
  4. An Adaptive, Parallel, and Inexact Newton Method for Large-scale Nonlinear Optimal Control
    Luke Bhan, Michael W. Mahoney, Sen Na
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. Degree Stability of Parallel Greedy Matching in Random Graphs
    Vishvajeet N, Shrinidhi Teganahally Sridhara
    arXivPreprintCC BY-SA 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{fekete2026tolerance,
  title = {{Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge-Kutta Methods}},
  author = {Imre Fekete and Ferenc Izsák and Vendel P. Kupás and Gustaf Söderlind},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32881},
  eprint = {2609.32881},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32881},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge-Kutta Methods
AU  - Imre Fekete
AU  - Ferenc Izsák
AU  - Vendel P. Kupás
AU  - Gustaf Söderlind
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32881
UR  - https://arxiv.org/abs/2609.32881
AB  - 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.
ER  -