Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations:
Abstract: "For the numerical integration of a stiff ordinary differential equation, fully implicit Runge-Kutta methods offer nice properties, like a high classical order and high stage order as well as an excellent stability behaviour. However, such methods need the solution of a set of highly...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1991
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1991,17 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "For the numerical integration of a stiff ordinary differential equation, fully implicit Runge-Kutta methods offer nice properties, like a high classical order and high stage order as well as an excellent stability behaviour. However, such methods need the solution of a set of highly coupled equations for the stage values and this is a considerable computational task. This paper discusses an iteration scheme to tackle this problem. By means of a suitable choice of the iteration parameters, the implicit relations for the stage values, as they occur in each iteration, can be uncoupled so that they can be solved in parallel The resulting scheme can be cast into the class of Diagonally Implicit Runge-Kutta (DIRK) methods and, similar to these methods, requires only one LU-factorization per step (per processor). The stability as well as the computational efficiency of the process strongly depends on the particular choice of the iteration parameters and on the number of iterations performed. We discuss several choices to obtain good stability and fast convergence. Based on these approaches, we wrote two codes possessing local error control and stepsize variation. We have implemented both codes on an ALLIANT/FX4 machine (four parallel vector processors and shared memory) and measured their speedup factors for a number of test problems Furthermore, the performance of these codes is compared with the performance of the best stiff ODE codes for sequential computers, like SIMPLE, LSODE and RADAU5. |
| Beschreibung: | 19 S. |
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| 100 | 1 | |a Sommeijer, Ben P. |d ca. 20. Jh. |e Verfasser |0 (DE-588)132820269 |4 aut | |
| 245 | 1 | 0 | |a Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| 264 | 1 | |a Amsterdam |c 1991 | |
| 300 | |a 19 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1991,17 | |
| 520 | 3 | |a Abstract: "For the numerical integration of a stiff ordinary differential equation, fully implicit Runge-Kutta methods offer nice properties, like a high classical order and high stage order as well as an excellent stability behaviour. However, such methods need the solution of a set of highly coupled equations for the stage values and this is a considerable computational task. This paper discusses an iteration scheme to tackle this problem. By means of a suitable choice of the iteration parameters, the implicit relations for the stage values, as they occur in each iteration, can be uncoupled so that they can be solved in parallel | |
| 520 | 3 | |a The resulting scheme can be cast into the class of Diagonally Implicit Runge-Kutta (DIRK) methods and, similar to these methods, requires only one LU-factorization per step (per processor). The stability as well as the computational efficiency of the process strongly depends on the particular choice of the iteration parameters and on the number of iterations performed. We discuss several choices to obtain good stability and fast convergence. Based on these approaches, we wrote two codes possessing local error control and stepsize variation. We have implemented both codes on an ALLIANT/FX4 machine (four parallel vector processors and shared memory) and measured their speedup factors for a number of test problems | |
| 520 | 3 | |a Furthermore, the performance of these codes is compared with the performance of the best stiff ODE codes for sequential computers, like SIMPLE, LSODE and RADAU5. | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1991,17 |w (DE-604)BV010177152 |9 1991,17 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006765076 | ||
Datensatz im Suchindex
| _version_ | 1804124583532429312 |
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| any_adam_object | |
| author | Sommeijer, Ben P. ca. 20. Jh |
| author_GND | (DE-588)132820269 |
| author_facet | Sommeijer, Ben P. ca. 20. Jh |
| author_role | aut |
| author_sort | Sommeijer, Ben P. ca. 20. Jh |
| author_variant | b p s bp bps |
| building | Verbundindex |
| bvnumber | BV010183348 |
| ctrlnum | (OCoLC)27260937 (DE-599)BVBBV010183348 |
| format | Book |
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| id | DE-604.BV010183348 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:47:58Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006765076 |
| oclc_num | 27260937 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 19 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Sommeijer, Ben P. ca. 20. Jh. Verfasser (DE-588)132820269 aut Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations Amsterdam 1991 19 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1991,17 Abstract: "For the numerical integration of a stiff ordinary differential equation, fully implicit Runge-Kutta methods offer nice properties, like a high classical order and high stage order as well as an excellent stability behaviour. However, such methods need the solution of a set of highly coupled equations for the stage values and this is a considerable computational task. This paper discusses an iteration scheme to tackle this problem. By means of a suitable choice of the iteration parameters, the implicit relations for the stage values, as they occur in each iteration, can be uncoupled so that they can be solved in parallel The resulting scheme can be cast into the class of Diagonally Implicit Runge-Kutta (DIRK) methods and, similar to these methods, requires only one LU-factorization per step (per processor). The stability as well as the computational efficiency of the process strongly depends on the particular choice of the iteration parameters and on the number of iterations performed. We discuss several choices to obtain good stability and fast convergence. Based on these approaches, we wrote two codes possessing local error control and stepsize variation. We have implemented both codes on an ALLIANT/FX4 machine (four parallel vector processors and shared memory) and measured their speedup factors for a number of test problems Furthermore, the performance of these codes is compared with the performance of the best stiff ODE codes for sequential computers, like SIMPLE, LSODE and RADAU5. Differential equations Runge-Kutta formulas Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1991,17 (DE-604)BV010177152 1991,17 |
| spellingShingle | Sommeijer, Ben P. ca. 20. Jh Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations Differential equations Runge-Kutta formulas |
| title | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_auth | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_exact_search | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_full | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_fullStr | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_full_unstemmed | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_short | Parallel-iterated Runge-Kutta methods for stiff ordinary differential equations |
| title_sort | parallel iterated runge kutta methods for stiff ordinary differential equations |
| topic | Differential equations Runge-Kutta formulas |
| topic_facet | Differential equations Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT sommeijerbenp paralleliteratedrungekuttamethodsforstiffordinarydifferentialequations |