{
  "case": "Helmholtz angular configurations, independent full-system verification",
  "reference": "Chaumont-Frelet and Valentin (2020), section 6.2, DOI 10.1137/19M1255616",
  "scope": "Same physical problem and explicitly selected finite local spaces; verifies discrete fields, not historical Figure 6.5 ordinates.",
  "native_code": {
    "project": "FEniCS/DOLFINx",
    "version": "0.9.0",
    "source_url": "https://github.com/FEniCS/dolfinx/tree/v0.9.0",
    "module": "dolfinx.fem / UFL variational assembly",
    "application": "original independent verification application",
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    "native_trace_coordinates": "Independent Legendre basis or constant/cosine/sine span; Cartesian face numbering and normal signs are assembled independently. PyMHM trace transforms and local coupling matrices are not used.",
    "local_matrices": "Native UFL diffusion, negative mass, boundary impedance and exact incident-wave loads",
    "global_operator": "Full complex broken-pressure/physical-normal-flux saddle matrix; no static condensation",
    "comparison": "Native nodal coordinates mapped bijectively to physical PyMHM nodes; both real and imaginary field coefficients compared on every macrocell.",
    "norms": "Native UFL complex pressure/gradient error integration, compared with separately integrated PyMHM norms; exact pressure norm1, gradient normomega.",
    "native_quadrature_degree": 24,
    "pymhm_assembly_gauss_points": 10,
    "pymhm_error_gauss_points": 12
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