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A MATRIX DEPENDENT/ALGEBRAIC MULTIGRID APPROACH FOR EXTRUDED MESHES WITH APPLICATIONS TO ICE SHEET MODELING.

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Title: A MATRIX DEPENDENT/ALGEBRAIC MULTIGRID APPROACH FOR EXTRUDED MESHES WITH APPLICATIONS TO ICE SHEET MODELING.
Authors: TUMINARO, R.1 rstumin@sandia.gov, PEREGO, M.1 mperego@sandia.gov, TEZAUR, I.1 ikalash@sandia.gov, SALINGER, A.1 agsalin@sandia.gov, PRICE, S.2 sprice@lanl.gov
Source: SIAM Journal on Scientific Computing. 2016, Vol. 38 Issue 5, pC504-C532. 29p.
Subjects: Algebraic multigrid methods, Mesh networks, Ice sheets, Iterative methods (Mathematics), Intergovernmental Panel on Climate Change, Mathematical models
Abstract: A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. This facilitates integration of the solver with a variety of different extruded mesh applications. [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.)
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  Data: A MATRIX DEPENDENT/ALGEBRAIC MULTIGRID APPROACH FOR EXTRUDED MESHES WITH APPLICATIONS TO ICE SHEET MODELING.
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mesh+networks%22">Mesh networks</searchLink><br /><searchLink fieldCode="DE" term="%22Ice+sheets%22">Ice sheets</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Intergovernmental+Panel+on+Climate+Change%22">Intergovernmental Panel on Climate Change</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink>
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  Data: A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. This facilitates integration of the solver with a variety of different extruded mesh applications. [ABSTRACT FROM AUTHOR]
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  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: 10.1137/15M1040839
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        Text: English
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        PageCount: 29
        StartPage: C504
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      – SubjectFull: Algebraic multigrid methods
        Type: general
      – SubjectFull: Mesh networks
        Type: general
      – SubjectFull: Ice sheets
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Intergovernmental Panel on Climate Change
        Type: general
      – SubjectFull: Mathematical models
        Type: general
    Titles:
      – TitleFull: A MATRIX DEPENDENT/ALGEBRAIC MULTIGRID APPROACH FOR EXTRUDED MESHES WITH APPLICATIONS TO ICE SHEET MODELING.
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              Text: 2016
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