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On the implementation of parallel iterated Runge-Kutta methods on a transputer network

Hans De Meyer (UGent) , Marnix Van Daele (UGent) and Guido Vanden Berghe (UGent)
(1993) APPLIED NUMERICAL MATHEMATICS. 13(1-3). p.155-163
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Abstract
A parallel iterated Runge-Kutta formula (PIRK) of eighth order is implemented on a transputer network. Tests are carried out for different network configurations. Efficiently measures are obtained with respect to the corresponding sequential PIRK8 method and with respect to the standard sequential DOPRI8 algorithm. It turns out that execution times are affected by communication and synchronization aspects and also in some cases by the particular ordering in which certain numerical calculations are performed.
Keywords
PIRK METHODS, RUNGE-KUTTA METHODS, PARALLEL ALGORITHMS, TRANSPUTERS

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Chicago
De Meyer, Hans, Marnix Van Daele, and Guido Vanden Berghe. 1993. “On the Implementation of Parallel Iterated Runge-Kutta Methods on a Transputer Network.” Applied Numerical Mathematics 13 (1-3): 155–163.
APA
De Meyer, Hans, Van Daele, M., & Vanden Berghe, G. (1993). On the implementation of parallel iterated Runge-Kutta methods on a transputer network. APPLIED NUMERICAL MATHEMATICS, 13(1-3), 155–163. Presented at the 6th Conference of the Numerical Treatment of Differential Equation (NUMDIFF-6).
Vancouver
1.
De Meyer H, Van Daele M, Vanden Berghe G. On the implementation of parallel iterated Runge-Kutta methods on a transputer network. APPLIED NUMERICAL MATHEMATICS. 1993;13(1-3):155–63.
MLA
De Meyer, Hans, Marnix Van Daele, and Guido Vanden Berghe. “On the Implementation of Parallel Iterated Runge-Kutta Methods on a Transputer Network.” APPLIED NUMERICAL MATHEMATICS 13.1-3 (1993): 155–163. Print.
@article{203130,
  abstract     = {A parallel iterated Runge-Kutta formula (PIRK) of eighth order is implemented on a transputer network. Tests are carried out for different network configurations. Efficiently measures are obtained with respect to the corresponding sequential PIRK8 method and with respect to the standard sequential DOPRI8 algorithm. It turns out that execution times are affected by communication and synchronization aspects and also in some cases by the particular ordering in which certain numerical calculations are performed.},
  author       = {De Meyer, Hans and Van Daele, Marnix and Vanden Berghe, Guido},
  issn         = {0168-9274},
  journal      = {APPLIED NUMERICAL MATHEMATICS},
  keyword      = {PIRK METHODS,RUNGE-KUTTA METHODS,PARALLEL ALGORITHMS,TRANSPUTERS},
  language     = {eng},
  location     = {Halle, Germany},
  number       = {1-3},
  pages        = {155--163},
  title        = {On the implementation of parallel iterated Runge-Kutta methods on a transputer network},
  url          = {http://dx.doi.org/10.1016/0168-9274(93)90139-I},
  volume       = {13},
  year         = {1993},
}

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