The efficient computation of a numerical irreducible decomposition of a polynomial system requires the application of various different homotopies. Some homotopies run only in sequence while others may be applied concurrently. Load balancing and pipelining algorithms are implemented in PHCpack, to run on multicore shared memory computers, equipped with GPU accelerators. Recent results were published in the CASC 2018 Proceedings, volume 11077 of LNCS, pages 361-375, Springer-Verlag.
International Congress on Industrial and Applied Mathematics, minisymposium on Solving Multidimensional Polynomial Systems Numerically, 17 July 2019, Valencia, Spain