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Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.

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Title: Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.
Authors: Schiano Di Cola, Vincenzo1 (AUTHOR), Cuomo, Salvatore2 (AUTHOR), Severino, Gerardo3 (AUTHOR), Berardi, Marco1 (AUTHOR) marco_berardi@rocketmail.com
Source: Applied Numerical Mathematics. Dec2025, Vol. 218, p58-72. 15p.
Subjects: Algebraic multigrid methods, Finite volume method, Monte Carlo method, Porous materials, Random fields
Abstract: We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an L 2 -error lower than other, Gaussian-type, approximations. • Groundwater equation, accounting for the spatial variability of the conductivity, is solved within a stochastic framework. • AMG solver is used for facing groundwater flow driven by Dirac-type sink/source. • AMG methods achieve efficient solutions adopting a finite volume framework. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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.)
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DbLabel: Engineering Source
An: 188153508
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  Data: Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.
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  Data: <searchLink fieldCode="AR" term="%22Schiano+Di+Cola%2C+Vincenzo%22">Schiano Di Cola, Vincenzo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cuomo%2C+Salvatore%22">Cuomo, Salvatore</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Severino%2C+Gerardo%22">Severino, Gerardo</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Berardi%2C+Marco%22">Berardi, Marco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> marco_berardi@rocketmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Dec2025, Vol. 218, p58-72. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+volume+method%22">Finite volume method</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Porous+materials%22">Porous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Random+fields%22">Random fields</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an L 2 -error lower than other, Gaussian-type, approximations. • Groundwater equation, accounting for the spatial variability of the conductivity, is solved within a stochastic framework. • AMG solver is used for facing groundwater flow driven by Dirac-type sink/source. • AMG methods achieve efficient solutions adopting a finite volume framework. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.apnum.2025.06.015
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 58
    Subjects:
      – SubjectFull: Algebraic multigrid methods
        Type: general
      – SubjectFull: Finite volume method
        Type: general
      – SubjectFull: Monte Carlo method
        Type: general
      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Random fields
        Type: general
    Titles:
      – TitleFull: Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media.
        Type: main
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            NameFull: Schiano Di Cola, Vincenzo
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            NameFull: Cuomo, Salvatore
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            NameFull: Severino, Gerardo
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            NameFull: Berardi, Marco
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          Dates:
            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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              Value: 218
          Titles:
            – TitleFull: Applied Numerical Mathematics
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