Developer Notes

Layout Conventions

• Mono: ω, γ
• Diph: ω1, γ1, ω2, γ2

Canonical contiguous layouts are fast-pathed; arbitrary UnknownLayout is supported through block insertion helpers.

Why Identity Regularization

Halo/inactive rows are set to identity to keep assembled systems robust without changing index mappings.

Benefits:

• stable direct/iterative solves,
• simpler API (state layout is fixed),
• robust fresh/dead-cell handling in moving runs.

Inactive Row Handling

• activity is derived from capacity volume/interface measure and halo masks,
• inactive rows are projected to identity with zero RHS.

Adding a New BC / Interface Condition

1. Extend coefficient/value extraction in the relevant helper:
   • mono: _interface_diagonals_mono
   • diph: _interface_coupling_diph
2. Add/adjust assembly block terms.
3. Add fixed and moving tests.
4. Update docs/src/interface_conditions.md and docs/src/api.md.

Time-Dependent Sampling Rules

• Fixed geometry unsteady: operator sampled at t + θΔt.
• Moving geometry unsteady:
  • slab geometry from [t^n, t^{n+1}],
  • source/interface data: end-state for BE, θ-blend for θ < 1,
  • interface spatial sampling at slab C_γ.

Moving Geometry Build

_build_moving_slab! performs:

1. space moments at t^n and t^{n+1},
2. space-time moments on a 2-node slab,
3. reduction back to spatial operators/capacity for assembly.