Runge-Kutta methods and local uniform grid refinement:
Abstract: "Local uniform grid refinement (LUGR) is an adaptive grid technique for computing solutions of partial differential equations possessing sharp spatial transitions. Using nested, finer-and-finer uniform subgrids, the LUGR technique refines the space grid locally around these transition...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1990
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1990,22 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Local uniform grid refinement (LUGR) is an adaptive grid technique for computing solutions of partial differential equations possessing sharp spatial transitions. Using nested, finer-and-finer uniform subgrids, the LUGR technique refines the space grid locally around these transitions, so as to avoid discretization on a very fine grid covering the entire physical domain. This paper examines the LUGR technique for time-dependent problems when combined with static-regridding. Static-regridding means that in the course of the time evolution, the space grid is adapted at discrete times. The present paper considers the general class of Runge-Kutta methods for the numerical time integration Following the method of lines approach, we develop a mathematical framework for the general Runge-Kutta LUGR method applied to multi-space dimensional problems. We hereby focus on parabolic problems, but a considerable part of the examination applies to hyperbolic problems as well. Much attention is paid to the local error analysis. The central issue here is a 'refinement condition' which is to underly the refinement strategy. By obeying this condition, spatial interpolation errors are controlled in a manner that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation A diagonally-implicit Runge-Kutta method is discussed for illustration purposes, both theoretically and numerically. |
| Beschreibung: | 50 S. |
Internformat
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| 100 | 1 | |a Trompert, Ron A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Runge-Kutta methods and local uniform grid refinement |c R. A. Trompert ; J. G. Verwer |
| 264 | 1 | |a Amsterdam |c 1990 | |
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1990,22 | |
| 520 | 3 | |a Abstract: "Local uniform grid refinement (LUGR) is an adaptive grid technique for computing solutions of partial differential equations possessing sharp spatial transitions. Using nested, finer-and-finer uniform subgrids, the LUGR technique refines the space grid locally around these transitions, so as to avoid discretization on a very fine grid covering the entire physical domain. This paper examines the LUGR technique for time-dependent problems when combined with static-regridding. Static-regridding means that in the course of the time evolution, the space grid is adapted at discrete times. The present paper considers the general class of Runge-Kutta methods for the numerical time integration | |
| 520 | 3 | |a Following the method of lines approach, we develop a mathematical framework for the general Runge-Kutta LUGR method applied to multi-space dimensional problems. We hereby focus on parabolic problems, but a considerable part of the examination applies to hyperbolic problems as well. Much attention is paid to the local error analysis. The central issue here is a 'refinement condition' which is to underly the refinement strategy. By obeying this condition, spatial interpolation errors are controlled in a manner that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation | |
| 520 | 3 | |a A diagonally-implicit Runge-Kutta method is discussed for illustration purposes, both theoretically and numerically. | |
| 650 | 4 | |a Error analysis (Mathematics) | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 700 | 1 | |a Verwer, Jan |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1990,22 |w (DE-604)BV010177152 |9 1990,22 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006772560 | ||
Datensatz im Suchindex
| _version_ | 1804124596045086720 |
|---|---|
| any_adam_object | |
| author | Trompert, Ron A. Verwer, Jan |
| author_facet | Trompert, Ron A. Verwer, Jan |
| author_role | aut aut |
| author_sort | Trompert, Ron A. |
| author_variant | r a t ra rat j v jv |
| building | Verbundindex |
| bvnumber | BV010192565 |
| ctrlnum | (OCoLC)24807144 (DE-599)BVBBV010192565 |
| format | Book |
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| id | DE-604.BV010192565 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:10Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006772560 |
| oclc_num | 24807144 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 50 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Trompert, Ron A. Verfasser aut Runge-Kutta methods and local uniform grid refinement R. A. Trompert ; J. G. Verwer Amsterdam 1990 50 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1990,22 Abstract: "Local uniform grid refinement (LUGR) is an adaptive grid technique for computing solutions of partial differential equations possessing sharp spatial transitions. Using nested, finer-and-finer uniform subgrids, the LUGR technique refines the space grid locally around these transitions, so as to avoid discretization on a very fine grid covering the entire physical domain. This paper examines the LUGR technique for time-dependent problems when combined with static-regridding. Static-regridding means that in the course of the time evolution, the space grid is adapted at discrete times. The present paper considers the general class of Runge-Kutta methods for the numerical time integration Following the method of lines approach, we develop a mathematical framework for the general Runge-Kutta LUGR method applied to multi-space dimensional problems. We hereby focus on parabolic problems, but a considerable part of the examination applies to hyperbolic problems as well. Much attention is paid to the local error analysis. The central issue here is a 'refinement condition' which is to underly the refinement strategy. By obeying this condition, spatial interpolation errors are controlled in a manner that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation A diagonally-implicit Runge-Kutta method is discussed for illustration purposes, both theoretically and numerically. Error analysis (Mathematics) Runge-Kutta formulas Verwer, Jan Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1990,22 (DE-604)BV010177152 1990,22 |
| spellingShingle | Trompert, Ron A. Verwer, Jan Runge-Kutta methods and local uniform grid refinement Error analysis (Mathematics) Runge-Kutta formulas |
| title | Runge-Kutta methods and local uniform grid refinement |
| title_auth | Runge-Kutta methods and local uniform grid refinement |
| title_exact_search | Runge-Kutta methods and local uniform grid refinement |
| title_full | Runge-Kutta methods and local uniform grid refinement R. A. Trompert ; J. G. Verwer |
| title_fullStr | Runge-Kutta methods and local uniform grid refinement R. A. Trompert ; J. G. Verwer |
| title_full_unstemmed | Runge-Kutta methods and local uniform grid refinement R. A. Trompert ; J. G. Verwer |
| title_short | Runge-Kutta methods and local uniform grid refinement |
| title_sort | runge kutta methods and local uniform grid refinement |
| topic | Error analysis (Mathematics) Runge-Kutta formulas |
| topic_facet | Error analysis (Mathematics) Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT trompertrona rungekuttamethodsandlocaluniformgridrefinement AT verwerjan rungekuttamethodsandlocaluniformgridrefinement |