File size: 542 Bytes
785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | import Mathlib
namespace OAI
noncomputable section
namespace AngularEndpoint
def node (N j : ℕ) : ℝ := -1 + 2 * (j : ℝ) / (N : ℝ)
def boundary (N j : ℕ) : ℝ :=
if j = 0 then -1 else if j = N + 1 then 1 else
(node N (j - 1) + node N j) / 2
def alpha (N j : ℕ) : ℝ := (1 + (node N j) ^ 2) / 4
def beta (N j : ℕ) : ℝ := node N j / 2
def profile (q : ℝ) : ℝ := (q ^ 2 + q ^ 4) / 16
def radius (τ η : ℝ) (N j : ℕ) : ℝ :=
1 / 2 + τ ^ 2 * (profile (node N j) + η)
end AngularEndpoint
end
end OAI
|