Mesh Generation Rules¶

XdTd's BEM mesher does not ask you to enter element counts. It applies a fixed set of rules to the geometry at hand, anchored by physical features (fastener pitches, crack tips, user-forced overrides), and lets element counts emerge. The same geometry meshed at a different refinement level produces a denser or coarser mesh — but the rules that produced it are the same.

The rules below describe the engine's behavior at a high level. They mirror the actual order of operations in DtdDiscretizationEngine.run().

The mesh-refinement slider (0–4) maps to a table of divisors and factors:

Parameter	Role
`LooseSegmentDivisor`	`loose_size = perimeter / divisor`
`PatchBoundaryFactor`	Multiplier applied to loose size on patch boundaries
`StiffenerBoundaryFactor`	Multiplier applied to loose size on stiffener boundaries
`CrackElements`	Number of elements per crack edge
`SegmentStartMultiplier`	Initial-element-size kick when growing from an anchor
`SegmentEndMultiplier`	Geometric growth ratio along a one-anchored segment

Element counts downstream are derived by applying those rules to local geometry. The user never enters element counts directly.

Rule 2 — Forced overrides win, and are applied before the engine starts¶

Any edge with forced_discretization > 0 is pre-meshed at its endpoints with size length / forced. The engine treats those endpoints as anchors and never overwrites them. Everything else flows around the override.

Rule 3 — Fastened stiffeners are discretized first, anchored at their pitch¶

Each fastened stiffener is collapsed into a single full-length combined edge (not two half-length segments) so only the total number of elements has to be even. Element size = fastener pitch; both endpoints come out of step 1 already meshed at 2 × pitch. Fastened-stiffener pitches are the very first anchors in the mesh — everything else propagates around them.

Rule 4 — Cracks are discretized second, in `CrackElements` segments per edge¶

If cracks exist, discretize_crack_tip_segments runs next. Each crack edge gets exactly CrackElements elements (a small integer set by the slider). Crack-tip endpoints become the next layer of anchors.

Rule 5 — The mesh propagates from anchored points outward, never from empty space¶

After the seed anchors (fastened-stiffener pitches + crack tips + forced overrides), the engine walks outward in a fixed priority:

Both endpoints anchored. Interpolate element sizes between the two known sizes.
One endpoint anchored. Initial element size = anchor × (1 + SegmentStart%), then grow each subsequent element by × (1 + SegmentEnd%) toward the loose end (geometric progression).
Re-check (1) after every pass. Newly-meshed endpoints may have promoted other segments to the both-anchored category.

Rule 6 — Loose segments (anchors at neither end) are discretized last¶

Default element size = perimeter / LooseSegmentDivisor. Then:

Patch boundaries: size × PatchBoundaryFactor
Stiffener boundaries (bonded, no crack): size × StiffenerBoundaryFactor
Clamped to [perimeter / (divisor × 7), perimeter / (divisor / 3)] — the absolute min/max guardrails.
Virtual edges (DRM / body-force regions) are processed before other loose segments at the unmodified loose size.

Rule 7 — Bonded stiffeners stay loose unless a crack reaches them¶

Bonded stiffener endpoints are not pre-anchored. If a crack intersects, the crack-tip anchor pulls the bonded stiffener mesh toward crack-element size on that side, and Rule 5 grows the rest outward. Otherwise they fall through to Rule 6 and get a uniform mesh at the loose size × stiffener factor.

Rule 8 — The engine loops until no progress is made, then exits cleanly¶

Steps in Rules 4–6 repeat. If a pass produces no new discretized segments, a warning is logged and the engine exits — there is no infinite loop. Any leftover undiscretized segments are reported as a warning rather than silently dropped.

Rule 9 — Internal points are computed off the finished boundary mesh¶

Internal points are not part of the discretization engine. They are generated afterwards from a boundary spacing field:

Each boundary node's local size is the average of its two adjacent edge lengths.
Hole-boundary sizes (cracks, internal boundaries) are capped at the median external-boundary size so coarse holes still attract a reasonable interior-point density.
Interior target spacing grows linearly with distance from the nearest boundary: local_size + 0.2 × distance.

Rule 10 — Counts emerge; they are not chosen¶

Two consequences worth keeping in mind:

Two identical geometries with different crack positions mesh differently, because the anchor topology differs.
Two identical configurations at different refinement levels mesh differently, because the divisors and CrackElements differ.

Refinement is a property of the rule set, not of any single edge.