`Admissible`

definition

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module: IndisputableMonolith.MaxwellDEC
domain: MaxwellDEC
line: 84 · github
papers citing: none yet

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IndisputableMonolith.MaxwellDEC on GitHub at line 84.

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formal source

  81  fun s => ω s * (h ▸ (HasHodge.star (k:=2) ω)) s
  82
  83/-- Admissibility: strictly positive material parameters. -/
  84def Admissible [HasHodge α] (M : Medium α) : Prop := 0 < M.eps ∧ 0 < M.mu
  85
  86/-- Positivity of the Hodge energy density for admissible media, provided the
  87    instance supplies `star2_psd`. This is signature-agnostic and delegates the
  88    sign choice to the instance via `star2_psd`. -/
  89theorem energy2_nonneg_pointwise
  90  [inst : HasHodge α] (h : inst.n - 2 = 2) (M : Medium α) (hadm : Admissible (α:=α) M) (ω : DForm α 2)
  91  : ∀ s, 0 ≤ energy2 (α:=α) ω h s := by
  92  intro s
  93  have hpsd := HasHodge.star2_psd (α:=α) h ω s
  94  simp [energy2]
  95  exact hpsd
  96
  97/-- PEC boundary descriptor (edges where tangential E vanishes). -/
  98structure PEC (β : Type) where
  99  boundary1 : Set (Simplex β 1)
 100
 101end MaxwellDEC
 102end IndisputableMonolith

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