Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems:
Abstract: "For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on 'parallelism across the problem', 'parallelism across the method' and on 'parallelism across the steps'. The first typ...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
1993
|
| Series: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1993,13 |
| Subjects: | |
| Summary: | Abstract: "For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on 'parallelism across the problem', 'parallelism across the method' and on 'parallelism across the steps'. The first type of parallelism does not require special integration methods and can be exploited within any available IVP solver. The method-parallelism approach received much attention, particularly within the class of explicit Runge-Kutta methods originating from fixed point iteration of implicit Runge-Kutta methods of Gaussian type. The construction and implementation on a parallel machine of such methods is extremely simple Since the computational work per processor is modest with respect to the number of data to be exchanged between the various processors, this type of parallelism is most suitable for shared memory systems. The required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor of 2. The third type of parallelism (step- parallelism) can be achieved in any IVP solver based on predictor-corrector iteration and requires the processors to communicate after each full iteration. If the iterations have sufficient computational volume, then the step-parallel approach may be suitable for implementation on distributed memory systems Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The dynamic step-parallel iteration process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to achieve speed-up factors up to 15. |
| Physical Description: | 15 S. |
Staff View
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| 245 | 1 | 0 | |a Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems |c P. J. van der Houwen ; B. P. Sommeijer ; W. A. van der Veen |
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| 520 | 3 | |a Abstract: "For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on 'parallelism across the problem', 'parallelism across the method' and on 'parallelism across the steps'. The first type of parallelism does not require special integration methods and can be exploited within any available IVP solver. The method-parallelism approach received much attention, particularly within the class of explicit Runge-Kutta methods originating from fixed point iteration of implicit Runge-Kutta methods of Gaussian type. The construction and implementation on a parallel machine of such methods is extremely simple | |
| 520 | 3 | |a Since the computational work per processor is modest with respect to the number of data to be exchanged between the various processors, this type of parallelism is most suitable for shared memory systems. The required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor of 2. The third type of parallelism (step- parallelism) can be achieved in any IVP solver based on predictor-corrector iteration and requires the processors to communicate after each full iteration. If the iterations have sufficient computational volume, then the step-parallel approach may be suitable for implementation on distributed memory systems | |
| 520 | 3 | |a Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The dynamic step-parallel iteration process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to achieve speed-up factors up to 15. | |
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| 700 | 1 | |a Sommeijer, Ben P. |d ca. 20. Jh. |e Verfasser |0 (DE-588)132820269 |4 aut | |
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| id | DE-604.BV010187969 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:04Z |
| institution | BVB |
| language | English |
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| physical | 15 S. |
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| spelling | Houwen, Pieter J. van der Verfasser aut Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems P. J. van der Houwen ; B. P. Sommeijer ; W. A. van der Veen Amsterdam 1993 15 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1993,13 Abstract: "For the parallel integration of nonstiff initial value problems (IVPs), three main approaches can be distinguished: approaches based on 'parallelism across the problem', 'parallelism across the method' and on 'parallelism across the steps'. The first type of parallelism does not require special integration methods and can be exploited within any available IVP solver. The method-parallelism approach received much attention, particularly within the class of explicit Runge-Kutta methods originating from fixed point iteration of implicit Runge-Kutta methods of Gaussian type. The construction and implementation on a parallel machine of such methods is extremely simple Since the computational work per processor is modest with respect to the number of data to be exchanged between the various processors, this type of parallelism is most suitable for shared memory systems. The required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor of 2. The third type of parallelism (step- parallelism) can be achieved in any IVP solver based on predictor-corrector iteration and requires the processors to communicate after each full iteration. If the iterations have sufficient computational volume, then the step-parallel approach may be suitable for implementation on distributed memory systems Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The dynamic step-parallel iteration process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to achieve speed-up factors up to 15. Runge-Kutta formulas Sommeijer, Ben P. ca. 20. Jh. Verfasser (DE-588)132820269 aut Veen, W. A. van der Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1993,13 (DE-604)BV010177152 1993,13 |
| spellingShingle | Houwen, Pieter J. van der Sommeijer, Ben P. ca. 20. Jh Veen, W. A. van der Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems Runge-Kutta formulas |
| title | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems |
| title_auth | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems |
| title_exact_search | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems |
| title_full | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems P. J. van der Houwen ; B. P. Sommeijer ; W. A. van der Veen |
| title_fullStr | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems P. J. van der Houwen ; B. P. Sommeijer ; W. A. van der Veen |
| title_full_unstemmed | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems P. J. van der Houwen ; B. P. Sommeijer ; W. A. van der Veen |
| title_short | Parallel iteration across the steps of high order Runge-Kutta methods forn onstiff initial value problems |
| title_sort | parallel iteration across the steps of high order runge kutta methods forn onstiff initial value problems |
| topic | Runge-Kutta formulas |
| topic_facet | Runge-Kutta formulas |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT houwenpieterjvander paralleliterationacrossthestepsofhighorderrungekuttamethodsfornonstiffinitialvalueproblems AT sommeijerbenp paralleliterationacrossthestepsofhighorderrungekuttamethodsfornonstiffinitialvalueproblems AT veenwavander paralleliterationacrossthestepsofhighorderrungekuttamethodsfornonstiffinitialvalueproblems |