Geometry, regions, materials and meshes

Geometry and material semantics are physics inputs, not renderer-specific data. The same physical object and region intent must be lowered to the selected FDM or FEM realization.

The first public scope covers geometry objects, transforms, region membership, material fields, interfaces, FDM grids, FEM meshes, airboxes, periodicity, remeshing and invalidation.

FDM uses structured cells, masks and grid ownership. FEM uses elements, material markers, boundary markers and shared domains. These representations differ while the public region and material meaning stays the same.

The initial public fixtures are a rectangular object, a thin film and a shared-domain airbox. Each fixture must expose mesh or grid identity, material regions, boundary policy and a reproducible build report.

Physical model

The public geometry contract describes a physical domain Omega, its magnetic subdomains Omega_i and material fields assigned to those subdomains. A discretization must preserve the declared region membership and boundary markers:

\[ Omega = union_i Omega_i, qquad Omega_i intersection Omega_j = emptyset for i != j \]

This is the partition contract, not a claim that every overlapping authoring operation is valid. Overlap resolution, interfaces and boolean operations must be documented explicitly before a mesh is qualified.

API and ProblemIR impact

The public authoring model must carry object geometry, transforms, region identity, material assignment, discretization policy, boundary policy and mesh provenance. The planner resolves FDM grid or FEM mesh capabilities without changing physical region meaning. Geometry changes invalidate mesh-dependent artifacts; magnetization changes do not by themselves invalidate mesh identity.

Validation strategy

The first fixtures are planned, not yet qualified:

  1. a rectangular object with one material region;

  2. a thin film with through-thickness discretization;

  3. a shared-domain magnetic object and airbox;

  4. a region mutation followed by remesh and certificate comparison.

Evidence must include mesh or grid identity, region markers, boundary policy and a reproducible build report. No result is currently claimed by this page.

Known limits and deferred work

This page does not yet qualify adaptive refinement, all boolean geometry operations, every periodic boundary combination or every mixed FEM topology. Those topics remain deferred until their public API, certificates and validation artifacts are linked.