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)

SLIDE 2

Motivation

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

SLIDE 3

Background

Biconnectivity
Articulation points
Meshes
Potential articulation points
“Double hinges”

SLIDE 4

The Ice-Sheet problem

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

SLIDE 5

Label Propagation

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

SLIDE 6

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

SLIDE 7

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.

SLIDE 8

Example

SLIDE 9

Incomplete Propagation

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

SLIDE 10

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)

SLIDE 11

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

SLIDE 12

Lowest Common Ancestor Heuristic

SLIDE 13

Distributed Memory

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

SLIDE 14

Distributed Memory

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

SLIDE 15

Current State

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