  We critically assess the performance of several variants of dual and
dual-primal domain decomposition strategies in problems with fixed subdomain
partitioning and high heterogeneity in stiffness coefficients typically arising
in topology optimization of modular structures. Our study considers Total FETI
and FETI Dual-Primal methods along with three enhancements: k-scaling, full
orthogonalization of the search directions, and considering multiple
search-direction at once, which gives us twelve variants in total. We test
these variants both on academic examples and snapshots of topology optimization
iterations. Based on the results, we conclude that (i) the original methods
exhibit very slow convergence in the presence of severe heterogeneity in
stiffness coefficients, which makes them practically useless, (ii) the full
orthogonalization enhancement helps only for mild heterogeneity, and (iii) the
only robust method is FETI Dual-Primal with multiple search direction and
k-scaling.
