heatΒΆ
pymor-demo heat [ARGS]
2D heat equation demo.
Discretization of the PDE:
\[\begin{split}\begin{align*}
\partial_t z(x, y, t) &= \Delta z(x, y, t), & 0 < x, y < 1,\ t > 0 \\
-\nabla z(0, y, t) \cdot n &= z(0, y, t) - u(t), & 0 < y < 1, t > 0 \\
-\nabla z(1, y, t) \cdot n &= z(1, y, t), & 0 < y < 1, t > 0 \\
-\nabla z(x, 0, t) \cdot n &= z(x, 0, t), & 0 < x < 1, t > 0 \\
-\nabla z(x, 1, t) \cdot n &= z(x, 1, t), & 0 < x < 1, t > 0 \\
z(x, y, 0) &= 0 & 0 < x, y < 1 \\
y(t) &= \int_0^1 z(1, y, t) dy, & t > 0
\end{align*}\end{split}\]
where \(u(t)\) is the input and \(y(t)\) is the output.
Parameters:
DIAMETER, --diameterDiameter option for the domain discretizer. [Default:
0.1]R, --rOrder of the ROMs. [Default:
5]