Keeping a thin layer

A graded block with a designed thin first layer, smoothed unprotected and with that layer kept by KeepLayer.

First-layer mean thickness change, in % (zero keeps the design)

Key points

• The cube-seeking metric thickens a designed layer: unprotected, the first layer grows by 137 % on average and up to 271 %.

• KeepLayer(wall, 1) keeps it exactly: 0.0 % change; the 98 kept vertices move by exactly 0.

• Protecting a layer moves the problem to its edge: the largest size jump between face-neighbours is 1.65 with KeepLayer against 1.23 unprotected (input 1.37).

The numbers

Check a layer by its thickness: the scaled Jacobian reads 1 for a box-shaped hex of any aspect ratio.

variant	first layer, mean change (%)	max change (%)	kept vertices, max move	size ratio max	inverted	min SJ	mean SJ
input	—	—	—	1.37	0	0.2129	0.7560
unprotected	+137.4	+271.1	—	1.23	0	0.7591	0.9004
KeepLayer	+0.0	+0.0	0	1.65	0	0.8122	0.9304

Bold: the best value in each column among the results (highest scaled Jacobian; lowest count, objective, time, change or distance); the input row is for reference.

Run python examples/smoother/hex/04_thin_layer.py to reproduce; it prints these numbers.