faq.md

FAQ

Q1: Does the input pattern foo.obj need to have a unit bbox? What happens if it is a periodic structure but with vertices ranging from 0 ot 100 e.g.

Graphs are rescaled to the cube $$[-1, 1]^3$$ immediately after reading them.

Q2: How to set the initial_params as well as radiusBounds / translationBounds / blendingBounds? Do you really need the translationBounds?

I'd recommend using pattern_optimization/GenIsosurfaceJob to specify bounds/initial parameters:

GenIsosurfaceJob $MICRO_DIR/patterns/3D/reference_wires/pattern0646.wire  -r'0.04,0.2' -o'-0.3,0.3' -e '1,0'

Here I'm applying offsetBounds instead of translationBounds. These constrain each vertex coordinate to remain within 0.3 of its original value from the .wire file. GenIsosurfaceJob translates this constraint into a pair of bounds on each translation variable, as you can see in the output. These per-variable bounds will override the translationBounds.

GenIsosurfaceJob also creates an initial parameter vector for you: it positions each vertex as in the .wire file and assigns all vertices a default radius and blending parameter of 0.07 and 0.01 respectively.

Q3: What is the effect of the parameter --usePthRoot?

Passing --usePthRoot changes the objective from $$\int_\Omega \mathrm{wcs}^p dx$$ to $$(\int_\Omega \mathrm{wcs}^p dx)^{1/p}$$. Using the p^th root prevents the objective from blowing up as the $$p$$ parameter is increased, simplifying parameter tuning for multi-objective optimization (e.g., if you wanted to add --proximityRegularizationWeight). But if you're simply simply minimizing the worst-case stress objective with an equality constraint on the elasticity tensor, omitting -P probably will work.

Q4: Do you need to fiddle around with the meshing options (-M), or did you use the same ones for all your tests?

I used the same meshing options for all 3D examples in the paper.

Q5: Once you've run WCSOptimization_cli, you are left on std::cout with a Final p: <whatever>, which I am assuming are the final result produced by the optimizer.

I generally didn't run the optimization to completion (partially because the runtimes on HPC varied wildly; on the old cluster, some nodes would occasionally run 2-10x slower for no apparent reason). Instead, I searched through the optimizer output to find the best stress reduction among the iterates within some threshold distance of the target moduli.

Q6: It seems that isosurface_inflator/ can be used to recover the final microstructure mesh (and not just the symmetry tet/triangle)? If so, could you indicate how you run it, given the results from WCSOptimization (for both 2D and 3D)?

Yes, you can use isosurface_cli to create a mesh for the optimal parameters (which you pass using the --params flag):

isosurface_cli 2D_orthotropic $MICRO_DIR//patterns/2D/topologies/0098.obj --params "<whitespace-separated params>" output_mesh.msh -m meshing_options.json

If you already have a mesh of the orthotropic cell (possibly with associated scalar/vector fields), you can use isosurface_inflator/replicate to produce the full period cell mesh. But, apart from visualization/printing, the orthotropic cell mesh should suffice for most operations (as long as you pass the -O flag to PeriodicHomogenization_cli, WCS_cli, ConstStrainDisplacement_cli, etc).

Q7: What is the difference between the options reflectiveInflator and generateFullPeriodCell in IsosurfaceInflator? Aren't they redundant?

They’re not redundant, but perhaps they should be named better.

• If generateFullPeriodCell and reflectiveInflator are true, then if the pattern has orthotropic symmetries, the positive quadrant/octant are meshed and then reflected to the full period cell.
• If generateFullPeriodCell is true and reflectiveInflator is false, then the full period cell is meshed directly.
• If generateFullPeriodCell is false and reflectiveInflator is true, then only the positive quadrant/octant mesh is returned.
• Can’t remember what happens in the false/false case.