Coarse-grain Parallelisation of Multi-imlicit Runge-kutta Methods Workpackage Wp5.3 Pasca (parallel Algorithms and Scalability)
نویسنده
چکیده
Introduction PACT Abstract A parallel implementation for multi-implicit Runge-Kutta methods with real eigen-values is described. The parallel method is analysed and the algorithm is devised. For the problem with d domains, the amount within the s-stage Runge-Kutta method, associated with the solution of system, is proportional to (sd) 3. The proposed parallelisation transforms the above system to s independent subsystems of dimension d. The amount of work for the solution of such systems is proportional to sd 3. The solution of d dimensional subsystems is the most complex operation within the Runge-Kutta method. The described parallel algorithm enable to solve each subsystem on a separate processor or on a separate set of processors.
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Coarse-Grain Parallelisation of Multi-Implicit Runge-Kutta Methods
A parallel implementation for a multi-implicit Runge-Kutta method (MIRK) with real eigenvalues is decribed. The parallel method is analysed and the algorithm is devised. For the problem with d domains , the amount of work within the s-stage MIRK method, associated with the solution of system, is proportional to (sd) 3 , in contrast to the simple implicit nite diierence method (IFD) where the am...
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