`Medium`

definition

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module: IndisputableMonolith.MaxwellDEC
domain: MaxwellDEC
line: 42 · github
papers citing: none yet

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open lean source

IndisputableMonolith.MaxwellDEC on GitHub at line 42.

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formal source

  39    0 ≤ x s * (h ▸ (star x)) s
  40
  41/-- Linear medium parameters. -/
  42structure Medium (α : Type) [HasHodge α] where
  43  eps : ℝ
  44  mu  : ℝ
  45
  46/-- Sources (charge and current). -/
  47structure Sources (α : Type) where
  48  ρ : DForm α 0
  49  J : DForm α 1
  50
  51variable {α : Type}
  52
  53/-- Quasi-static Maxwell equations on the mesh (no time derivative terms).
  54    Faraday and Gauss-M are stated cleanly. Constitutive relations (const_D, const_B)
  55    and source equations (ampere_qs, gauss_e) require dimension n=3 for form-degree
  56    alignment, so they are parameterized by the dimension hypothesis `hn`. -/
  57structure Equations (α : Type) [HasCoboundary α] [inst : HasHodge α] (M : Medium α) where
  58  E : DForm α 1
  59  H : DForm α 1
  60  B : DForm α 2
  61  D : DForm α 2
  62  src : Sources α
  63  /-- Faraday QS: curl E = 0 (no time-varying B in quasistatic limit) -/
  64  faraday_qs : HasCoboundary.d E = fun _ => 0
  65  /-- Ampere QS: d H = star J (requires n-1=2 for form-degree alignment) -/
  66  ampere_qs  : ∀ (hn : inst.n - 1 = 2),
  67    HasCoboundary.d H = cast (congrArg (DForm α) hn) (HasHodge.star src.J)
  68  /-- Gauss E: d D = star rho (requires n-0=3 for form-degree alignment) -/
  69  gauss_e    : ∀ (hn : inst.n - 0 = 3),
  70    HasCoboundary.d D = cast (congrArg (DForm α) hn) (HasHodge.star src.ρ)
  71  /-- Gauss M: div B = 0 (no magnetic monopoles) -/
  72  gauss_m    : HasCoboundary.d B = fun _ => 0

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