On Robust multigrid methods for non-smooth variational problems:
Abstract: "We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non-smooth problem is how to represent the nonlinearit...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1996
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| Schriftenreihe: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1996,38 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non-smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation." |
| Beschreibung: | 19 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Kornhuber, Ralf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a On Robust multigrid methods for non-smooth variational problems |c Ralf Kornhuber |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1996 | |
| 300 | |a 19 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 1996,38 | |
| 520 | 3 | |a Abstract: "We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non-smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation." | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Multigrid methods (Numerical analysis) | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t Preprint SC |v 1996,38 |w (DE-604)BV004801715 |9 1996,38 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010357965 | |
Datensatz im Suchindex
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| author | Kornhuber, Ralf |
| author_facet | Kornhuber, Ralf |
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| author_variant | r k rk |
| building | Verbundindex |
| bvnumber | BV017186790 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)37235519 (DE-599)BVBBV017186790 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV017186790 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010357965 |
| oclc_num | 37235519 |
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| physical | 19 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Kornhuber, Ralf Verfasser aut On Robust multigrid methods for non-smooth variational problems Ralf Kornhuber Berlin Konrad-Zuse-Zentrum für Informationstechnik 1996 19 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1996,38 Abstract: "We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non-smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation." Boundary value problems Finite element method Multigrid methods (Numerical analysis) Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 1996,38 (DE-604)BV004801715 1996,38 |
| spellingShingle | Kornhuber, Ralf On Robust multigrid methods for non-smooth variational problems Boundary value problems Finite element method Multigrid methods (Numerical analysis) |
| title | On Robust multigrid methods for non-smooth variational problems |
| title_auth | On Robust multigrid methods for non-smooth variational problems |
| title_exact_search | On Robust multigrid methods for non-smooth variational problems |
| title_full | On Robust multigrid methods for non-smooth variational problems Ralf Kornhuber |
| title_fullStr | On Robust multigrid methods for non-smooth variational problems Ralf Kornhuber |
| title_full_unstemmed | On Robust multigrid methods for non-smooth variational problems Ralf Kornhuber |
| title_short | On Robust multigrid methods for non-smooth variational problems |
| title_sort | on robust multigrid methods for non smooth variational problems |
| topic | Boundary value problems Finite element method Multigrid methods (Numerical analysis) |
| topic_facet | Boundary value problems Finite element method Multigrid methods (Numerical analysis) |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT kornhuberralf onrobustmultigridmethodsfornonsmoothvariationalproblems |