How short can SIMP penalty continuation be and still remove the dependence on the starting density field?

research/simdesign-contlength

How short can SIMP penalty continuation be and still remove the start dependence? A ramp of 25 iterations or fewer leaves much of it (worst start differs in 16–23% of elements, 27–31% for a fixed penalty); 50 iterations cuts compliance spread to 0.01–0.23%, and a 112-iteration ramp is most repeatable but ends at a worse compliance (stylised, 2D, 150 iterations).

5 tests

What it found

Follow-up to simdesign-starts. Half-MBB, volume 0.5, final p = 3, exactly 150 OC iterations, random starts (noise ±0.3; 20 on 60×20, 12 on 90×30), with the penalty ramped 1 → 3 over 0, 6, 12, 25, 50, 75 or 112 iterations. Ramps of 25 iterations or fewer leave most of the start dependence of a fixed penalty (worst start differs from the uniform-start design in 31% and 27% of elements on the two meshes): for ramps of 6–25 it is still 17–23% (60×20) and 16–20% (90×30), and compliance spreads 0.5–1.3%. At 50 iterations the spread falls to 0.01% (60×20) and 0.23% (90×30); at 75 the median disagreement is 0.0–0.3%. A 112-iteration ramp is the most repeatable but gives a worse final compliance (203.55 against 203.08 on 60×20; 197.3 against 196.6 on 90×30), because few iterations remain at full penalty. Stylised: 2D, one problem, two meshes, 150 iterations, not run to convergence.

A figure from its own output

Figure produced by research/simdesign-contlength: ramp — simdesign-contlength/experiments/ramp.png, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.