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ON AN ADAPTIVE MULTIGRID SOLVER FOR CONVECTION-DOMINATED PROBLEMS.

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Title: ON AN ADAPTIVE MULTIGRID SOLVER FOR CONVECTION-DOMINATED PROBLEMS.
Authors: Dahmen, Wolfgang, Müller, Siegfried, Schlinkmann, Thomas
Source: SIAM Journal on Scientific Computing. 2001, Vol. 23 Issue 3, p781. 24p.
Subjects: Heat equation, Transfer operators
Abstract: The objective of this paper is to develop and describe an adaptive multigrid scheme for the numerical solution of convection-diffusion-reaction equations with dominating convection or reaction term. Specifically, we propose a systematic construction of problem and scale-dependent restriction, prolongation and smoothing operators in combination with an adaptive mesh refinement strategy. In particular, adaptivity is not only to reduce computational complexity but also to stabilize standard Galerkin discretizations so that adding artificial viscosity can be avoided. The approach is suited for any choice of underlying multiresolution sequences, in particular for standard finite element discretizations on nested but possibly nonuniform meshes. Moreover, all concepts are in principle independent of the spatial dimension and avoid any special flow-dependent enumeration of unknowns. The performance of the scheme is illustrated by various examples in one and two spatial dimensions. They are chosen so as to exhibit possibly many types of adverse or singular behavior in connection with constant and varying convection or the interplay between convective and reactive terms. In the light of these tests those issues are identified that require further research. [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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  Data: ON AN ADAPTIVE MULTIGRID SOLVER FOR CONVECTION-DOMINATED PROBLEMS.
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  Data: The objective of this paper is to develop and describe an adaptive multigrid scheme for the numerical solution of convection-diffusion-reaction equations with dominating convection or reaction term. Specifically, we propose a systematic construction of problem and scale-dependent restriction, prolongation and smoothing operators in combination with an adaptive mesh refinement strategy. In particular, adaptivity is not only to reduce computational complexity but also to stabilize standard Galerkin discretizations so that adding artificial viscosity can be avoided. The approach is suited for any choice of underlying multiresolution sequences, in particular for standard finite element discretizations on nested but possibly nonuniform meshes. Moreover, all concepts are in principle independent of the spatial dimension and avoid any special flow-dependent enumeration of unknowns. The performance of the scheme is illustrated by various examples in one and two spatial dimensions. They are chosen so as to exhibit possibly many types of adverse or singular behavior in connection with constant and varying convection or the interplay between convective and reactive terms. In the light of these tests those issues are identified that require further research. [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/S106482759935544X
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        Text: English
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      – TitleFull: ON AN ADAPTIVE MULTIGRID SOLVER FOR CONVECTION-DOMINATED PROBLEMS.
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              Text: 2001
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