From 4c570ba4b023a1e34c46a9e7833dff70862f3d2b Mon Sep 17 00:00:00 2001
From: Helge Gehring <42973196+HelgeGehring@users.noreply.github.com>
Date: Wed, 11 Oct 2023 15:11:11 -0700
Subject: [PATCH] add thermal simple to toc

---
 docs/_toc.yml                |  1 +
 docs/julia/thermal_simple.jl | 16 ++++++++++++++--
 2 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/docs/_toc.yml b/docs/_toc.yml
index d0f172c5..7ffd77e2 100644
--- a/docs/_toc.yml
+++ b/docs/_toc.yml
@@ -45,6 +45,7 @@ parts:
     - file: julia/waveguide_anisotropic.jl
     - file: julia/waveguide_overlap_integral.jl
     - file: julia/lithium_niobate_phase_shifter.jl
+    - file: photonics/examples/thermal_simple.jl
 
   - caption: Benchmarks
     chapters:
diff --git a/docs/julia/thermal_simple.jl b/docs/julia/thermal_simple.jl
index 998ba4b1..a9ea7164 100644
--- a/docs/julia/thermal_simple.jl
+++ b/docs/julia/thermal_simple.jl
@@ -15,7 +15,7 @@
 # ---
 
 # %% [markdown]
-# # Mode solving
+# # Match theoretical model for electro-optic simulation
 
 # %% tags=["hide-input", "thebe-init"]
 using Gridap
@@ -24,6 +24,11 @@ using Gridap.Geometry
 using Femwell.Maxwell.Electrostatic
 using Femwell.Thermal
 
+# %% [markdown]
+# We start with setting up a square domain.
+# For the boundary conditions, we tag the left and the right side of the model.
+# Furthermore, we create a function which returns 1 indipendent of the tag which is the parameter to descrie the constants of the simplified model.
+
 # %% tags=["hide-output"]
 domain = (0, 1, 0, 1)
 partition = (20, 20)
@@ -37,6 +42,13 @@ dΩ = Measure(Ω, 1)
 τ = CellField(tags, Ω)
 constant = tag -> 1
 
+# %% [markdown]
+# ## Electrostatic
+# The first step ist to calculate the potential.
+# For this we solve the electrostatic equation $Δϕ = 0$ and define the voltage at two oppositing boundaries to 0V at $x=0$ and 1V at $x=1$.
+# The theoretical solution of this function is a linear function.
+# $$ ϕ(x)=x $$
+
 # %% tags=["hide-input"]
 p0 = compute_potential(constant ∘ τ, Dict("left" => 0.0, "right" => 1.0))
 
@@ -65,7 +77,7 @@ T_transient = calculate_temperature_transient(
     Dict("boundary" => 0.0),
     temperature(T0),
     1e-4,
-    1.e-3,
+    1e-3,
 )
 sums = [(t, ∑(∫(u)dΩ) / ∑(∫(1)dΩ)) for (u, t) in T_transient]
 println(sums)