Energy calculation while simulation

[GenB31415]

While simulating the Brusselator (with spatial coupling) with u(x, y, t) and v(x, y, t), I have to calculate the energy
W(t) = integral ((u ^ 2 + v ^ 2) dxdy) (or other analogous quantities) at times t < tFin. How do I access the local values u(x, y, t) and v(x, y, t) during the simulation (run-time) to have W(t) for the later use? Is there a general technique? Thanks.

[david-zwicker]

The most straight-forward way would probably to use a DataTracker to call a custom function periodically.
Here is a modification of the example that shows the ideas in action:

from pde import PDE, FieldCollection, DataTracker, ScalarField, UnitGrid
import matplotlib.pyplot as plt

# define the PDE
a, b = 1, 3
d0, d1 = 1, 0.1
eq = PDE(
    {
        "u": f"{d0} * laplace(u) + {a} - ({b} + 1) * u + u**2 * v",
        "v": f"{d1} * laplace(v) + {b} * u - u**2 * v",
    }
)

# initialize state
grid = UnitGrid([64, 64])
u = ScalarField(grid, a, label="Field $u$")
v = b / a + 0.1 * ScalarField.random_normal(grid, label="Field $v$")
state = FieldCollection([u, v])


def get_energy(data):
    u, v = data
    return (u**2 + v**2).integral

# simulate the pde
data_tracker = DataTracker(get_energy, interval=1)
eq.solve(state, t_range=20, dt=1e-3, tracker=['progress', data_tracker])

plt.plot(data_tracker.times, data_tracker.data)

[GenB31415]

For my case it works fine. Thank you!

[GenB31415]

In my case this solution works fine after minor corrections 1. from pde import PDE, FieldCollection, PlotTracker, ScalarField, UnitGrid, DataTracker <<-- add DataTracker 2. pde.DataTracker(  <<--- DataTracker(  omit  pde. Thank you! On Tuesday, May 4, 2021, 12:50:55 PM CDT, David Zwicker ***@***.***> wrote: The most straight-forward way would probably to use a DataTracker to call a custom function periodically. Here is a modification of the example that shows the ideas in action: from pde import PDE, FieldCollection, PlotTracker, ScalarField, UnitGrid import matplotlib.pyplot as plt # define the PDE a, b = 1, 3 d0, d1 = 1, 0.1 eq = PDE( { "u": f"{d0} * laplace(u) + {a} - ({b} + 1) * u + u**2 * v", "v": f"{d1} * laplace(v) + {b} * u - u**2 * v", } ) # initialize state grid = UnitGrid([64, 64]) u = ScalarField(grid, a, label="Field $u$") v = b / a + 0.1 * ScalarField.random_normal(grid, label="Field $v$") state = FieldCollection([u, v]) def get_energy(data): u, v = data return (u**2 + v**2).integral # simulate the pde data_tracker = pde.DataTracker(get_energy, interval=1) eq.solve(state, t_range=20, dt=1e-3, tracker=['progress', data_tracker]) plt.plot(data_tracker.times, data_tracker.data) — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[GenB31415]

I'd like to extend this solution to see both plots: 2D and the energy in the same time. The idea is to use the trackers as in the examples. My code is below

from pde import PDE, FieldCollection, PlotTracker, ScalarField, UnitGrid, DataTracker
import matplotlib.pyplot as plt

define the PDE

a, b = 1, 3
d0, d1 = 1, 0.1
eq = PDE(
{
"u": f"{d0} * laplace(u) + {a} - ({b} + 1) * u + u2 * v",
"v": f"{d1} * laplace(v) + {b} * u - u2 * v",
}
)

initialize state

grid = UnitGrid([64, 64])
u = ScalarField(grid, a, label="Field $u$")
v = b / a + 0.1 * ScalarField.random_normal(grid, label="Field $v$")
state = FieldCollection([u, v])
def get_energy(data):
u, v = data
return (u2 + v2).integral

showThis=False
#showThis=True # it is interesting that dependently of comment/uncomment this string I see only one of plots!
trackers = [
"progress", # show progress bar during simulation
#storage.tracker(interval=1), # store data every simulation time unit
PlotTracker(show=showThis), # show images during simulation
DataTracker(get_energy),
]
eq.solve(state, t_range=5, dt=1e-3, tracker=trackers)
data_tracker = trackers[2]
print(data_tracker.times)
plt.plot(data_tracker.times, data_tracker.data, marker="o" )
plt.grid(True); plt.xlabel("Time"); plt.ylabel("Energy"); plt.title("Plot")
plt.show()

My question is as follows: dependently of comment/uncomment of the string (#showThis=True) I see one of the plots! But how to see both plots of the field and the energy in the same time? Thank you.

[david-zwicker]

This is not implemented. If you want to implement it yourself, you can hook into the simulation using a CallbackTracker

[GenB31415]

Thanks