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Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.

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Title: Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.
Authors: Jiang, Lei1 (AUTHOR) leijiang@hnu.edu.cn, Yang, Haijian2 (AUTHOR) haijianyang@hnu.edu.cn, Shi, Lijuan1 (AUTHOR) lijuanshi@hnu.edu.cn, Tu, Jiali1 (AUTHOR) jltu@hnu.edu.cn
Source: SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pB440-B465. 26p.
Subjects: Schur complement, Geological carbon sequestration, Domain decomposition methods, Nonlinear equations, Carbon sequestration, Multiphase flow, Parallel programming
Abstract: High-resolution reservoir simulation of multiphase and multicomponent porous media flows, arising from geological carbon sequestration, requires solving large, sparse nonlinear and linear systems efficiently on parallel computers. This multiphysical process involves a compositional flow model with multiple wells and corner-point grid geometry, which demands efficient and scalable solvers optimized for high-performance computing. In the study, we present a nonstandard restricted additive Schwarz preconditioner with Schur complement, called SchurRAS, to mitigate slow convergence and stagnation in solving sparse linear systems. Our hybrid preconditioning approach combines overlapping domain decomposition for parallel scalability with localized Schur complement approximations to enhance solver efficiency on distributed-memory systems equipped with multicore nodes. Moreover, a minimum-type semismooth Newton algorithm is proposed to enhance nonlinear convergence and enforce physical constraints. Large-scale simulations are conducted on geological reservoir benchmarks and real-field carbon sequestration projects. The parallel performance evaluation on a supercomputer demonstrates the scalability of our approach to thousands of processor cores and shows that SchurRAS outperforms standard RAS in both iteration count and computational time. [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: 195222027
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.
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  Data: <searchLink fieldCode="AR" term="%22Jiang%2C+Lei%22">Jiang, Lei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> leijiang@hnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Haijian%22">Yang, Haijian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> haijianyang@hnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Shi%2C+Lijuan%22">Shi, Lijuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lijuanshi@hnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Tu%2C+Jiali%22">Tu, Jiali</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jltu@hnu.edu.cn</i>
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  Data: <searchLink fieldCode="DE" term="%22Schur+complement%22">Schur complement</searchLink><br /><searchLink fieldCode="DE" term="%22Geological+carbon+sequestration%22">Geological carbon sequestration</searchLink><br /><searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Carbon+sequestration%22">Carbon sequestration</searchLink><br /><searchLink fieldCode="DE" term="%22Multiphase+flow%22">Multiphase flow</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink>
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  Label: Abstract
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  Data: High-resolution reservoir simulation of multiphase and multicomponent porous media flows, arising from geological carbon sequestration, requires solving large, sparse nonlinear and linear systems efficiently on parallel computers. This multiphysical process involves a compositional flow model with multiple wells and corner-point grid geometry, which demands efficient and scalable solvers optimized for high-performance computing. In the study, we present a nonstandard restricted additive Schwarz preconditioner with Schur complement, called SchurRAS, to mitigate slow convergence and stagnation in solving sparse linear systems. Our hybrid preconditioning approach combines overlapping domain decomposition for parallel scalability with localized Schur complement approximations to enhance solver efficiency on distributed-memory systems equipped with multicore nodes. Moreover, a minimum-type semismooth Newton algorithm is proposed to enhance nonlinear convergence and enforce physical constraints. Large-scale simulations are conducted on geological reservoir benchmarks and real-field carbon sequestration projects. The parallel performance evaluation on a supercomputer demonstrates the scalability of our approach to thousands of processor cores and shows that SchurRAS outperforms standard RAS in both iteration count and computational time. [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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        Value: 10.1137/25M1780183
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      – Code: eng
        Text: English
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        PageCount: 26
        StartPage: B440
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      – SubjectFull: Schur complement
        Type: general
      – SubjectFull: Geological carbon sequestration
        Type: general
      – SubjectFull: Domain decomposition methods
        Type: general
      – SubjectFull: Nonlinear equations
        Type: general
      – SubjectFull: Carbon sequestration
        Type: general
      – SubjectFull: Multiphase flow
        Type: general
      – SubjectFull: Parallel programming
        Type: general
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      – TitleFull: Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.
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            NameFull: Jiang, Lei
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            NameFull: Yang, Haijian
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            NameFull: Shi, Lijuan
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            NameFull: Tu, Jiali
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            – D: 01
              M: 05
              Text: 2026
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              Y: 2026
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