“Multi-time-step integration”的意思、由来-开放百科全书

In numerical analysis, multi-time-step integration, also referred to as multiple-step or asynchronous time integration, is a numerical time-integration method that uses different time-steps or time-integrators for different parts of the problem. There are different approaches to multi-time-step integration. They are based on domain decompostition^[1]^[2] and can be classified into strong (monolithic) or weak (staggered) schemes.^[3] Using different time-steps or time-integrators in the context of a weak algorithm is rather straightforward, because the numerical solvers operate independently. However, this is not the case in a strong algorithm. In the past few years a number of research articles have addressed the development of strong multi-time-step algorithms.^[4]^[5]^[6]^[7] In either case, strong or weak, the numerical accuracy and stability needs to be carefully studied. Other approaches to multi-time-step integration in the context of operator splitting methods have also been developed; i.e., multi-rate GARK method and multi-step methods for molecular dynamics simulations.^[8]

1. ^{{Cite book|url=https://global.oup.com/academic/product/domain-decomposition-methods-for-partial-differential-equations-9780198501787?cc=us&lang=en&|title=Domain Decomposition Methods for Partial Differential Equations|isbn=9780198501787|publisher=Oxford University Press|date=1999-07-29|series=Numerical Mathematics and Scientific Computation}}
2. ^{{Cite book|title=Domain Decomposition Methods — Algorithms and Theory – Springer|volume = 34|last=Toselli|first=Andrea|last2=Widlund|first2=Olof B.|doi=10.1007/b137868|series = Springer Series in Computational Mathematics|year = 2005|isbn = 978-3-540-20696-5}}
3. ^{{Cite journal|last=Felippa|first=Carlos A.|last2=Park|first2=K. C.|last3=Farhat|first3=Charbel|date=2001-03-02|title=Partitioned analysis of coupled mechanical systems|journal=Computer Methods in Applied Mechanics and Engineering|series=Advances in Computational Methods for Fluid-Structure Interaction|volume=190|issue=24–25|pages=3247–3270|doi=10.1016/S0045-7825(00)00391-1|bibcode=2001CMAME.190.3247F}}
4. ^{{Cite journal|last=Gravouil|first=Anthony|last2=Combescure|first2=Alain|date=2001-01-10|title=Multi-time-step explicit–implicit method for non-linear structural dynamics|url=http://onlinelibrary.wiley.com/doi/10.1002/1097-0207(20010110)50:13.0.CO;2-A/abstract|journal=International Journal for Numerical Methods in Engineering|language=en|volume=50|issue=1|pages=199–225|doi=10.1002/1097-0207(20010110)50:13.0.CO;2-A|issn=1097-0207|doi-broken-date=2019-03-15}}
5. ^{{Cite journal|last=Prakash|first=A.|last2=Hjelmstad|first2=K. D.|date=2004-12-07|title=A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics|journal=International Journal for Numerical Methods in Engineering|language=en|volume=61|issue=13|pages=2183–2204|doi=10.1002/nme.1136|issn=1097-0207|bibcode=2004IJNME..61.2183P}}
6. ^{{Cite journal|last=Karimi|first=S.|last2=Nakshatrala|first2=K. B.|date=2014-09-15|title=On multi-time-step monolithic coupling algorithms for elastodynamics|journal=Journal of Computational Physics|volume=273|pages=671–705|doi=10.1016/j.jcp.2014.05.034|arxiv=1305.6355|bibcode=2014JCoPh.273..671K}}
7. ^{{Cite journal|last=Karimi|first=S.|last2=Nakshatrala|first2=K. B.|date=2015-01-01|title=A monolithic multi-time-step computational framework for first-order transient systems with disparate scales|journal=Computer Methods in Applied Mechanics and Engineering|volume=283|pages=419–453|doi=10.1016/j.cma.2014.10.003|arxiv=1405.3230|bibcode=2015CMAME.283..419K}}
8. ^{{Cite journal|last=Jia|first=Zhidong|last2=Leimkuhler|first2=Ben|date=2006-01-01|title=Geometric integrators for multiple time-scale simulation|url=http://stacks.iop.org/0305-4470/39/i=19/a=S04|journal=Journal of Physics A: Mathematical and General|language=en|volume=39|issue=19|pages=5379|doi=10.1088/0305-4470/39/19/S04|issn=0305-4470|bibcode=2006JPhA...39.5379J}}

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