Multilevel, extrapolation and sparse grid methods:
Abstract: "Multigrid Methods are asymptotically optimal solvers for discretized partial differential equations (PDE). For the optimal solutions of PDEs, however, the quality of the discretization is of the same importance as the speed of the algebraic solution process. Especially for high accur...
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
München
1993
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| Series: | Technische Universität <München>: TUM-I
9319 |
| Subjects: | |
| Summary: | Abstract: "Multigrid Methods are asymptotically optimal solvers for discretized partial differential equations (PDE). For the optimal solutions of PDEs, however, the quality of the discretization is of the same importance as the speed of the algebraic solution process. Especially for high accuracy requirements, high order discretizations become increasingly attractive. We describe higher order techniques, like extrapolation and sparse grid combination that are particularly interesting in the context of multilevel algorithms, because they are based on discretizing the problems on grids with different mesh sizes. Classical Richardson extrapolation can be extended and generalized in many ways. One generalization is to consider the mesh widths in the different coordinate directions as distinct parameters. This leads to the so-called multivariate extrapolation and the combination technique." |
| Physical Description: | 15 S. graph. Darst. |
Staff View
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| 100 | 1 | |a Rüde, Ulrich |d 1957- |e Verfasser |0 (DE-588)111660041 |4 aut | |
| 245 | 1 | 0 | |a Multilevel, extrapolation and sparse grid methods |c Ulrich Rüde |
| 264 | 1 | |a München |c 1993 | |
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| 490 | 1 | |a Technische Universität <München>: TUM-I |v 9319 | |
| 490 | 1 | |a Sonderforschungsbereich Methoden und Werkzeuge für die Nutzung Paralleler Rechnerarchitekturen: SFB-Bericht / A |v 1993,10 | |
| 520 | 3 | |a Abstract: "Multigrid Methods are asymptotically optimal solvers for discretized partial differential equations (PDE). For the optimal solutions of PDEs, however, the quality of the discretization is of the same importance as the speed of the algebraic solution process. Especially for high accuracy requirements, high order discretizations become increasingly attractive. We describe higher order techniques, like extrapolation and sparse grid combination that are particularly interesting in the context of multilevel algorithms, because they are based on discretizing the problems on grids with different mesh sizes. Classical Richardson extrapolation can be extended and generalized in many ways. One generalization is to consider the mesh widths in the different coordinate directions as distinct parameters. This leads to the so-called multivariate extrapolation and the combination technique." | |
| 650 | 4 | |a Differential equations, Partial | |
| 810 | 2 | |a A |t Sonderforschungsbereich Methoden und Werkzeuge für die Nutzung Paralleler Rechnerarchitekturen: SFB-Bericht |v 1993,10 |w (DE-604)BV004627888 |9 1993,10 | |
| 830 | 0 | |a Technische Universität <München>: TUM-I |v 9319 |w (DE-604)BV006185376 |9 9319 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006051784 | ||
Record in the Search Index
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| author | Rüde, Ulrich 1957- |
| author_GND | (DE-588)111660041 |
| author_facet | Rüde, Ulrich 1957- |
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| author_sort | Rüde, Ulrich 1957- |
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| bvnumber | BV009130219 |
| ctrlnum | (OCoLC)32526788 (DE-599)BVBBV009130219 |
| format | Book |
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| id | DE-604.BV009130219 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:31:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006051784 |
| oclc_num | 32526788 |
| open_access_boolean | |
| owner | DE-29T DE-12 DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-12 DE-91G DE-BY-TUM |
| physical | 15 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| record_format | marc |
| series | Technische Universität <München>: TUM-I |
| series2 | Technische Universität <München>: TUM-I Sonderforschungsbereich Methoden und Werkzeuge für die Nutzung Paralleler Rechnerarchitekturen: SFB-Bericht / A |
| spelling | Rüde, Ulrich 1957- Verfasser (DE-588)111660041 aut Multilevel, extrapolation and sparse grid methods Ulrich Rüde München 1993 15 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Technische Universität <München>: TUM-I 9319 Sonderforschungsbereich Methoden und Werkzeuge für die Nutzung Paralleler Rechnerarchitekturen: SFB-Bericht / A 1993,10 Abstract: "Multigrid Methods are asymptotically optimal solvers for discretized partial differential equations (PDE). For the optimal solutions of PDEs, however, the quality of the discretization is of the same importance as the speed of the algebraic solution process. Especially for high accuracy requirements, high order discretizations become increasingly attractive. We describe higher order techniques, like extrapolation and sparse grid combination that are particularly interesting in the context of multilevel algorithms, because they are based on discretizing the problems on grids with different mesh sizes. Classical Richardson extrapolation can be extended and generalized in many ways. One generalization is to consider the mesh widths in the different coordinate directions as distinct parameters. This leads to the so-called multivariate extrapolation and the combination technique." Differential equations, Partial A Sonderforschungsbereich Methoden und Werkzeuge für die Nutzung Paralleler Rechnerarchitekturen: SFB-Bericht 1993,10 (DE-604)BV004627888 1993,10 Technische Universität <München>: TUM-I 9319 (DE-604)BV006185376 9319 |
| spellingShingle | Rüde, Ulrich 1957- Multilevel, extrapolation and sparse grid methods Technische Universität <München>: TUM-I Differential equations, Partial |
| title | Multilevel, extrapolation and sparse grid methods |
| title_auth | Multilevel, extrapolation and sparse grid methods |
| title_exact_search | Multilevel, extrapolation and sparse grid methods |
| title_full | Multilevel, extrapolation and sparse grid methods Ulrich Rüde |
| title_fullStr | Multilevel, extrapolation and sparse grid methods Ulrich Rüde |
| title_full_unstemmed | Multilevel, extrapolation and sparse grid methods Ulrich Rüde |
| title_short | Multilevel, extrapolation and sparse grid methods |
| title_sort | multilevel extrapolation and sparse grid methods |
| topic | Differential equations, Partial |
| topic_facet | Differential equations, Partial |
| volume_link | (DE-604)BV004627888 (DE-604)BV006185376 |
| work_keys_str_mv | AT rudeulrich multilevelextrapolationandsparsegridmethods |