Parallel Implementation of Runge–Kutta Integrators with Low Storage Requirements
This paper considers the parallel solution of large systems of ordinary differential equations (ODEs) which possess a special access pattern by explicit Runge–Kutta (RK) methods. Such systems may arise, for example, from the semi-discretization of partial differential equations (PDEs). We propose an implementation strategy based on a pipelined processing of the stages of the RK method that does not impose restrictions on the choice of coefficients of the RK method. This approach can be implemented with low storage while still allowing efficient step control by embedded solutions.
KeywordsParallel Implementation Access Distance Stepsize Control Argument Vector Neighboring Processor
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- 4.Berland, J., Bogey, C., Bailly, C.: Optimized explicit schemes: matching and boundary schemes, and 4th-order Runge–Kutta algorithm. In: 10th AIAA/CEAS Aeroacoustics Conference, pp. 1–34 (2004), AIAA Paper 2004-2814Google Scholar
- 7.Kennedy, C.A., Carpenter, M.H.: Third-order 2N-storage Runge–Kutta schemes with error control. Technical Report NASA TM-109111, National Aeronautics and Space Administration, Langley Research Center, Hampton, VA (1994)Google Scholar