2.8. Diffusion on a Cartesian grid

This example shows how to solve the diffusion equation on a Cartesian grid.

  0%|          | 0/1.0 [00:00<?, ?it/s]
Initializing:   0%|          | 0/1.0 [00:00<?, ?it/s]
  0%|          | 0/1.0 [00:05<?, ?it/s]
  1%|          | 0.01/1.0 [00:05<08:40, 526.13s/it]
  3%|▎         | 0.03/1.0 [00:05<02:50, 175.39s/it]
  3%|▎         | 0.03/1.0 [00:05<02:50, 175.44s/it]
100%|██████████| 1.0/1.0 [00:05<00:00,  5.26s/it]
100%|██████████| 1.0/1.0 [00:05<00:00,  5.26s/it]

from pde import CartesianGrid, DiffusionPDE, ScalarField

grid = CartesianGrid([[-1, 1], [0, 2]], [30, 16])  # generate grid
state = ScalarField(grid)  # generate initial condition
state.insert([0, 1], 1)

eq = DiffusionPDE(0.1)  # define the pde
result = eq.solve(state, t_range=1, dt=0.01)
result.plot(cmap="magma")