Quantitative
Input : Surface mesh, background mesh and metric tensor on background mesh
|
|
Metric Complexity
|
# Vertices
|
# Elements
|
Time (s)
|
| Target
|
80,000
|
~160,000
|
~960,000
|
N/A
|
| AFLR (without metric alignment)
|
80,299.6
|
130,668
|
744,285
|
341.92
|
| AFLR (with metric alignment)
|
80,422.6
|
127,112
|
732,883
|
238.57
|
| CDT3D (1 thread)
|
78,215.9
|
189,788
|
1,107,104
|
100.0
|
| CDT3D (6 threads)
|
79,221.6
|
191,353
|
1,116,112
|
21.5
|
Input : background mesh and metric tensor on background mesh (tets 590,102 , vertices 103,781)
|
|
Metric Complexity
|
# Vertices
|
# Elements
|
Time (s)
|
| AFLR (without metric alignment)
|
|
|
|
|
|
| AFLR (with metric alignment)
|
79,666.1
|
116,024
|
664,501
|
15.130
|
| CDT3D (1 thread)
|
79333.4
|
126,877
|
727,840
|
38.134
|
| CDT3D (2 threads)
|
79,314.6
|
126,968
|
728,240
|
21.01
|
| CDT3D (4 threads)
|
79,312.3
|
127,207
|
729,640
|
12.38
|
Qualitative
Time Breakdown
| Operations
|
details
|
AFLR (malign =ON)
|
AFLR(maling =OFF)
|
| BG Mesh Initialization
|
|
0.534
|
0.533
|
| Point Creation
|
| Euclidean length
|
0.028
|
0.037
|
| Riemannian length
|
0.166
|
0.24
|
| Metric interpolation at face
|
0.302
|
0.408
|
| Evaluate Log(Metric)
|
1.902
|
0.272
|
| Search in BG mesh
|
137.825
|
334.594
|
| Search point in mesh
|
0.092
|
0.271
|
| Metric-Alignment
|
80.387
|
0
|
| Point Creation Total
|
219.759
|
336.881
|
| Point Filtering
|
|
2.373
|
2.412
|
| Point Insertion
|
|
0.154
|
0.184
|
| Element Deactivation
|
|
0.626
|
2.914
|
| Local Reconnection 32-23
|
|
8.553
|
9.037
|
| Local Reconnection 4-4
|
|
0
|
3.118
|
| Total
|
|
232.389
|
355.571
|
| Operations
|
CDT3D ( 1 thread )
|
| BG Mesh Initialization
|
1.08535
|
| Deactivate Elements
|
2.69843
|
| Point Creation
|
8.54597
|
| Point Insertion
|
0.25458
|
| Local Reconnection 3-2/2-3
|
64.4204
|
| Local Reconnection 4-4
|
22.4864
|
| Total
|
100.058
|
- Although CDT3D does not use alignment, it is not this that makes it faster (actually when alignment will be implemented, it is expected to make refinement even faster)
- By design, the point insertion order in CDT3D favours points that are geometrically close in space.
- In CDT3D, we store the previous location in BG mesh, speeding up subsequent queries in the same neighborhood.
