Supplemental Material for “ Parallel Computation of 3 D Morse - Smale complexes ”

Gradient and MS Complex on sub-domains. Gradient pairs are computed within a sub-domain using Algorithm 1 and Algorithm 2 from section 4. The cell complex of the sub-domain is extended to include the set of cells that are incident on the shared boundary of sub-domains but gradient pairs are computed only on the initial sub-domain cell complex (see Figure 1b). Thus, we obtain identical pairings for cells along the shared boundary when we process all subdomains that share the boundary cell. To facilitate merging we mark all gradient pairs that cross a shared boundary as critical (see Figure 1b).