Parallel shooting methods for finding periodic steady state solutions to models of machines with reciprocating pistons

Parallel single- and multiple shooting methods were tested for finding periodic steady state solutions to a Stirling engine model. The model was used to illustrate features of the methods and possibilities for optimisations.Performance was measured using simulation of an experimental data set as test case. A parallel speedup factor of 23 on 33 processors was achieved with multiple shooting. But fast transients at the beginnings of subintervals caused significant overhead for the multiple shooting methods and limited the best speedup to 3.8 relative to the fastest sequential method: Single shooting with reduced dimension of the boundary value problem.