Quad smoothing

Deep dives are the in-depth companion to the gallery: the gallery shows meshes, a deep dive explains one topic. More topics (topology, mesh metrics) will follow.

nekmeshpy.quadmesh.smoother moves a quad mesh’s vertices, never its connectivity, under constraints, and reports what it did (user guide). Two ways in:

  • Methods explains how the smoother works and when to use which part: Laplace smoothing, Winslow smoothing, the optimizer, constraints and projection, boundary layers.

  • Case studies shows it on real meshes; each page has a viewer (input left, the stage you pick right, coloured by scaled Jacobian) with a histogram and history of the per-quad scaled Jacobian.

Workflow

Each box links to the page that explains it.

1Check the inputcheck_connectivity refuses gaps; overlapping and inverted quads are reported
↓
2Attach geometry, set constraintsOnSurface / OnCurve / boundary=: the decision tree
↓
3Protect designed layersKeepLayer, SlideColumns, weights
↓
4Pick the methodsuggest_schedule by default
Laplace: a cheap passoptimizer: the shapeWinslow: concave or thin curved blocksTMOP (optional, MFEM): keeps the input's sizes and layers, ("tmop", {...})inverted quads: untangle_schedule(), an optimize preset with a wide-to-narrow delta
↓
5Run a round, read the reportpropose / accept / undo; numbers per region
↓ good enough
not yet: back to step 2, 3 or 4 (undo a worse round)
6High-order mesh?stays curved: the nodes follow the vertices; rebuild_high_order re-projects them onto the targets, then export; TMOP smooths a curved mesh as curved

Key points

  • Smoothing repairs a damaged mesh; it does not improve a good one. Inverted or perturbed inputs recover; a good mesh changes little, and some of its numbers can get worse.

  • A smoothed surface is not propagated into a hex mesh. Each case page’s hex section measures what carrying it in does.

  • Folded or overlapping input is a known limitation: a fold can persist.

  • High-order nodes are rebuilt (carried and projected) after the linear smoothing, not smoothed.

Regenerating the pages

  • Every case page is a run of a script in examples/smoother/quad/; the Methods pages run the smoother on their own inputs. The pages are static Markdown that include fragments from docs/smoother/quad/_generated/ and load docs/_static/smoother/quad/*_frames.json; the docs build only reads them, and no number is typed.

  • After the smoother or an example changes, regenerate and commit:

python docs/_ext/gen_smoother_quad_assets.py                    # every page, about a minute
python docs/_ext/gen_smoother_quad_assets.py 01_basics          # the frames of one script
python docs/_ext/gen_smoother_quad_hexviews_assets.py                # the hex views (carotid, U-tube, wire coil), about two minutes
python docs/_ext/gen_smoother_quad_methods_assets.py            # the Methods pages: comparison runs, tables, parameter tables