Ice-Sheet Meshes and Biconnectivity Ian Bogle (RPI), Karen Devine - PowerPoint PPT Presentation

Ice-Sheet Meshes and Biconnectivity Ian Bogle (RPI), Karen Devine (SNL), Mauro Perego (SNL), Siva Rajamanickam (SNL), George Slota (RPI)

Motivation https://insideclimatenews.org/sites/default/files/styles/icn_full_wrap_wide/public/getz-ice-shelf_jeremy-harbeck-nasa.jpg?itok=D1uLzpFu

Background • Biconnectivity • Articulation points • Meshes • Potential articulation points • “Double hinges”

The Ice-Sheet problem • Modeling Antarctic Ice-Sheet • “Grounding” • Degenerate Features • Similar to Biconnectivity

Label Propagation • Three pieces: • Grounding • Articulation point heuristic • No false negatives • Propagation rules • Propagate grounding throughout the mesh

Labels • Each node has a unique vertex ID • Labels contain four vertex IDs • Two for “grounded” nodes • Two for senders • Labels can be • Empty, no vertex IDs • Half-full, one pair of vertex IDs • Full, two pairs of vertex IDs • Nodes with full labels are considered grounded

Basic Propagation Rules • Potential Articulation Points • Pass own ID if grounded • Only pass label to neighbor once • Can pass label too early • All other nodes • Pass whole label unconditionally • Only pass labels from nodes whose labels have changed recently. • Since nodes only change twice, we visit each node at most twice.

Example

Incomplete Propagation • Due to potential articulation point restriction • Can be detected and fixed • Very rare in ice-sheet cases

Results vs. Biconnectivity Algorithms Ice-sheet resolution BCC-BFS BCC-Color Label Propagation 16 km 0.0163 (s) 0.0841 (s) 0.0046 (s) 8 km 0.0483 (s) 0.7728 (s) 0.0196 (s) 4 km 0.1912 (s) 7.6713 (s) 0.0834 (s) 2 km 0.7199 (s) 54.821 (s) 0.3395 (s) 1 km 3.3271 (s) - 1.3904 (s)

Generalizing to Biconnectivity • Need grounding and articulation point heuristic • Any two neighbors for grounding • LCA Heuristic • Propagation rules work fine • Only finds one biconnected component per propagation • Iterative

Lowest Common Ancestor Heuristic

Distributed Memory • The original problem exists in distributed memory • The propagation rules still work • Ice-sheet case is simple to distribute

Distributed Memory • Biconnectivity version is more difficult • Distribute LCA Heuristic • Strategically pick neighbors for the 2-Clique • Easier using Trilinos

Current State • Working on an MPI implementation • Work-efficient (?) distributed biconnectivity algorithm • Working to publish in ISC