DRAFT: Optimize Connectivity Construction

[philipc2]

Closes #1196 #1197

Overview

• Optimizes the construction of the following connectivity variables
  • edge_node_connectivity
  • face_edge_connectivity
  • face_face_connectivity
• Cleans up docstrings and setters in Grid

All timings below were taken on a single NCAR Derecho CPU node.

• AMD EPYC™ 7763 Milan processors
• Dual-socket nodes, 64 cores per socket
• 256 GB DDR4 memory per node

Connectivity Timing (Before)

Resolution	Nodes	Faces	Edges	edge_node & face_edge	face_face	edge_face
30km	1,310,720	655,362	1,966,080	9.37s	14.81s	0.05s
15km	5,242,880	2,621,442	7,864,320	39.99s	58.22s	0.23s
7.5km	5,242,880	2,621,442	7,864,320	99.31s	223.92s	0.50s

Connectivity Timings (After)

Resolution	Nodes	Faces	Edges	edge_node & face_edge	face_face	edge_face (unchanged)
30km	1,310,720	655,362	1,966,080	0.54	0.032s	0.05s
15km	5,242,880	2,621,442	7,864,320	2.79	0.123s	0.23s
7.5km	5,242,880	2,621,442	7,864,320	11.41	0.293s	0.50s

Connectivity Speedup

edge_node and face_edge connectivity

• 8.7x to 17.35x speedup

face_face

• 462x to 764x speedup