Iterated Runge-Kutta methods on parallel computers:
Abstract: "In this paper, we study diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers. These iteration methods are such that after a finite number of m iterations, the iterated Runge-Kutta method belongs to the class of dia...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1990
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1990,1 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "In this paper, we study diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers. These iteration methods are such that after a finite number of m iterations, the iterated Runge-Kutta method belongs to the class of diagonally implicit Runge-Kutta methods (DIRK methods) using mk implicit stages where k is the number of stages of the generating implicit Runge-Kutta methods (corrector method). However, a large number of the stages of this DIRK method can be computed in parallel, so that the number of stages that have to be computed sequentially is only m. The iteration parameters of the method are tuned in such a way that we get fast convergence to the stability characteristics of the corrector method By means of numerical experiments we show that also the solution produced by the resulting iteration method converges rapidly to the corrector solution so that both stability and accuracy characteristics are comparable with those of the corrector. This implies that the reduced accuracy often shown when itegrating stiff problems by means of DIRK methods already available in the literature (which is caused by a low stage order), is not shown by the DIRK methods developed in this paper provided that the corrector method has a sufficiently high stage order. Moreover, by iterating e.g. Radau correctors, we can construct methods of any order, whereas the order of accuracy of the conventionally constructed DIRK methods is limited to four. |
| Beschreibung: | 26 S. |
Internformat
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| 100 | 1 | |a Houwen, Pieter J. van der |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Iterated Runge-Kutta methods on parallel computers |c P. J. van der Houwen ; B. P. Sommeijer |
| 264 | 1 | |a Amsterdam |c 1990 | |
| 300 | |a 26 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1990,1 | |
| 520 | 3 | |a Abstract: "In this paper, we study diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers. These iteration methods are such that after a finite number of m iterations, the iterated Runge-Kutta method belongs to the class of diagonally implicit Runge-Kutta methods (DIRK methods) using mk implicit stages where k is the number of stages of the generating implicit Runge-Kutta methods (corrector method). However, a large number of the stages of this DIRK method can be computed in parallel, so that the number of stages that have to be computed sequentially is only m. The iteration parameters of the method are tuned in such a way that we get fast convergence to the stability characteristics of the corrector method | |
| 520 | 3 | |a By means of numerical experiments we show that also the solution produced by the resulting iteration method converges rapidly to the corrector solution so that both stability and accuracy characteristics are comparable with those of the corrector. This implies that the reduced accuracy often shown when itegrating stiff problems by means of DIRK methods already available in the literature (which is caused by a low stage order), is not shown by the DIRK methods developed in this paper provided that the corrector method has a sufficiently high stage order. Moreover, by iterating e.g. Radau correctors, we can construct methods of any order, whereas the order of accuracy of the conventionally constructed DIRK methods is limited to four. | |
| 650 | 4 | |a Parallel processing (Electronic computers) | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 700 | 1 | |a Sommeijer, Ben P. |d ca. 20. Jh. |e Verfasser |0 (DE-588)132820269 |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1990,1 |w (DE-604)BV010177152 |9 1990,1 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006767779 | ||
Datensatz im Suchindex
| _version_ | 1804124588083249152 |
|---|---|
| any_adam_object | |
| author | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh |
| author_GND | (DE-588)132820269 |
| author_facet | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh |
| author_role | aut aut |
| author_sort | Houwen, Pieter J. van der |
| author_variant | p j v d h pjvd pjvdh b p s bp bps |
| building | Verbundindex |
| bvnumber | BV010187112 |
| ctrlnum | (OCoLC)22291019 (DE-599)BVBBV010187112 |
| format | Book |
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| id | DE-604.BV010187112 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006767779 |
| oclc_num | 22291019 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 26 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Houwen, Pieter J. van der Verfasser aut Iterated Runge-Kutta methods on parallel computers P. J. van der Houwen ; B. P. Sommeijer Amsterdam 1990 26 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1990,1 Abstract: "In this paper, we study diagonally implicit iteration methods for solving implicit Runge-Kutta methods with high stage order on parallel computers. These iteration methods are such that after a finite number of m iterations, the iterated Runge-Kutta method belongs to the class of diagonally implicit Runge-Kutta methods (DIRK methods) using mk implicit stages where k is the number of stages of the generating implicit Runge-Kutta methods (corrector method). However, a large number of the stages of this DIRK method can be computed in parallel, so that the number of stages that have to be computed sequentially is only m. The iteration parameters of the method are tuned in such a way that we get fast convergence to the stability characteristics of the corrector method By means of numerical experiments we show that also the solution produced by the resulting iteration method converges rapidly to the corrector solution so that both stability and accuracy characteristics are comparable with those of the corrector. This implies that the reduced accuracy often shown when itegrating stiff problems by means of DIRK methods already available in the literature (which is caused by a low stage order), is not shown by the DIRK methods developed in this paper provided that the corrector method has a sufficiently high stage order. Moreover, by iterating e.g. Radau correctors, we can construct methods of any order, whereas the order of accuracy of the conventionally constructed DIRK methods is limited to four. Parallel processing (Electronic computers) Runge-Kutta formulas Sommeijer, Ben P. ca. 20. Jh. Verfasser (DE-588)132820269 aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1990,1 (DE-604)BV010177152 1990,1 |
| spellingShingle | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh Iterated Runge-Kutta methods on parallel computers Parallel processing (Electronic computers) Runge-Kutta formulas |
| title | Iterated Runge-Kutta methods on parallel computers |
| title_auth | Iterated Runge-Kutta methods on parallel computers |
| title_exact_search | Iterated Runge-Kutta methods on parallel computers |
| title_full | Iterated Runge-Kutta methods on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_fullStr | Iterated Runge-Kutta methods on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_full_unstemmed | Iterated Runge-Kutta methods on parallel computers P. J. van der Houwen ; B. P. Sommeijer |
| title_short | Iterated Runge-Kutta methods on parallel computers |
| title_sort | iterated runge kutta methods on parallel computers |
| topic | Parallel processing (Electronic computers) Runge-Kutta formulas |
| topic_facet | Parallel processing (Electronic computers) Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT houwenpieterjvander iteratedrungekuttamethodsonparallelcomputers AT sommeijerbenp iteratedrungekuttamethodsonparallelcomputers |