Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems

This paper considers incorporating a bound-consistency enforcing procedure to an interval branch-and-prune method. A heuristic to decide, when to use the developed operator, is proposed. As enforcing the bound-consistency is much more time consuming than performing other narrowing tools, we parallelize the procedure, using Intel TBB. A few parallelization versions are considered. Also, this is a good opportunity to make a case-study of performance of various lock instances, implemented in the TBB package. Numerical results for typical benchmark problems are presented and analyzed. A specific lock version, proper for the application, is proposed. Performance on two architectures is considered: Intel Xeon and Intel Xeon Phi (MIC).