Add minimal test to solve elliptic equation
Test to solve stationary heat equation in 2D with Dirichlet boundary conditions (fixed temperature):
- \kappa \Delta T = q \quad \mathrm{in} \quad \Omega\\
T = T_b \quad \mathrm{in} \quad \partial \Omega
The numerical scheme is a standard finite difference scheme (could be reinterpreted as a finite volume scheme):
- \kappa \left( \frac{T_{i+1,j} - 2 T_{i,j} + T_{i-1,j}}{{\Delta x}^2} + \frac{T_{i,j+1} - 2 T_{i,j} + T_{i,j-1}}{{\Delta y}^2} \right) = q_{i,j}
The number of unknowns in the matrix takes into account halo zones along with trivial equations:
T_{i,j} = T_b
Edited by thomas.padioleau