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Optimized Schwarz Methods for Heterogeneous Heat Transfer Problems.

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Title: Optimized Schwarz Methods for Heterogeneous Heat Transfer Problems.
Authors: Gander, Martin J.1 (AUTHOR) Martin.Gander@unige.ch, Lu, Liu-Di1 (AUTHOR) liudi.Lu@unige.ch, WU, Tingting2 (AUTHOR) wtting@nuaa.edu.cn
Source: SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pA1587-A1610. 24p.
Subjects: Diffusion coefficients, Domain decomposition methods, Mathematical analysis, Numerical analysis, Laplace transformation, Thermal conductivity, Boundary value problems
Abstract: We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive the error equation and obtain the convergence factor. The optimal transmission operators are nonlocal, and thus inconvenient to use in practice. We introduce three versions of local approximations for the transmission parameter, and provide a detailed analysis at the continuous level in each case to identify the best local transmission conditions. Numerical experiments are presented to illustrate the performance of each local transmission condition. As shown in our analysis, local transmission conditions, which are scaled appropriately with respect to the heterogeneous diffusion coefficients, are more efficient and robust especially when the discontinuity of the diffusion coefficient is large. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 195222018
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Optimized Schwarz Methods for Heterogeneous Heat Transfer Problems.
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 3, pA1587-A1610. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Diffusion+coefficients%22">Diffusion coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+transformation%22">Laplace transformation</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+conductivity%22">Thermal conductivity</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive the error equation and obtain the convergence factor. The optimal transmission operators are nonlocal, and thus inconvenient to use in practice. We introduce three versions of local approximations for the transmission parameter, and provide a detailed analysis at the continuous level in each case to identify the best local transmission conditions. Numerical experiments are presented to illustrate the performance of each local transmission condition. As shown in our analysis, local transmission conditions, which are scaled appropriately with respect to the heterogeneous diffusion coefficients, are more efficient and robust especially when the discontinuity of the diffusion coefficient is large. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1137/25M1763068
    Languages:
      – Code: eng
        Text: English
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        PageCount: 24
        StartPage: A1587
    Subjects:
      – SubjectFull: Diffusion coefficients
        Type: general
      – SubjectFull: Domain decomposition methods
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Laplace transformation
        Type: general
      – SubjectFull: Thermal conductivity
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
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      – TitleFull: Optimized Schwarz Methods for Heterogeneous Heat Transfer Problems.
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            NameFull: Lu, Liu-Di
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            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
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