# Mathematical background

The numerical foundation of MoCSI: how the heat equation is discretized, which boundary conditions are supported, and how solar radiation is coupled across facets.

<div class="box-container">
  <a class="box-card" href="finite_element_method.html">
    <span class="box-icon">🧮</span>
    <b>Finite Element Method</b>
    <span class="box-sub">Spatial discretization of the heat equation</span>
  </a>
  <a class="box-card" href="boundary_conditions.html">
    <span class="box-icon">📐</span>
    <b>Boundary conditions</b>
    <span class="box-sub">Top and bottom BC formulations available in MoCSI</span>
  </a>
  <a class="box-card" href="tdma_solver.html">
    <span class="box-icon">🔢</span>
    <b>TDMA solver</b>
    <span class="box-sub">Tridiagonal matrix algorithm for the 1D case</span>
  </a>
  <a class="box-card" href="radiosity.html">
    <span class="box-icon">☀️</span>
    <b>Radiosity</b>
    <span class="box-sub">Scattered light and self-heating between facets</span>
  </a>
</div>

```{toctree}
:hidden:
:maxdepth: 0

finite_element_method
boundary_conditions
tdma_solver
radiosity
```