Parallel processing of the solution of ordinary differential equations on a general purpose multiprocessor system OSCAR

This paper proposes an efficient parallel processing scheme for the solution of explicit ordinary differential equations. The calculations required for the solution of ordinary differential equations by the use of some numerical integration formulae generally involve arithmetic (scalar) assignment statements with complicated data dependencies. For the reason, no efficient parallel processing schemes have so far been developed. The parallel processing scheme proposed in this paper can attain minimum processing time with an arbitrary number of parallel processors by the use of the efficient static multiprocessor scheduling algorithms developed by the authors. Its practicality is confirmed on a general-purpose multiprocessor system named OSCAR (Optimally Scheduled Advanced Multiprocessor), which is being developed by the authors to extract advantageous features of scheduling algorithms to the maximum extent.