Author/Editor     Trobec, Roman; Orel, Bojan; Slivnik, Boštjan
Title     Coarse-grain parallelisation of multi-implicit Runge-Kutta methods
Type     članek
Source     In: Vulkov L, Wasniewski J, Yalamov P, editors. Numerical analysis and its applications. Proceedings of the 1st International workshop WNAA '96; 1996 Jun; Rousse, Bulgaria. Berlin Heidelberg: Springer,
Publication year     1997
Volume     str. 498-504
Language     eng
Abstract     A parallel implementation for a multi-implicint 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)2, in contrast to the simple implicit finite difference method (IFD) where the amount of work is proportional to d3. However, it is shown that s-stage MIRK admits much greater time steps for the same order of error. Additionally, the proposed parallelisation transforms the system of the dimension sd to s independent sub-systems of dimension d. The amount of work for the sequential solution of such systems is proportional to sd3. The described parallel algorithm enables the solving of each of the s subsystems on a separate processor; finally, the amount of work is again d3, but the profit of a larger time step still remains. To test the theory, a comparative example of the 3-D heat transfer in a human heart with 64 3 domains is shown and numerically calculated by 3-stage MIRK.
Descriptors     NUMERICAL ANALYSIS, COMPUTER-ASSISTED
MATHEMATICAL COMPUTING