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lmoresi merged 1 commit into from
Jun 24, 2026
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Make Poisson gradient recovery example script-safe #270

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156 changes: 88 additions & 68 deletions docs/examples/heat_transfer/basic/Ex_Poisson_Gradient_Recovery.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,8 +2,8 @@
"""
# 📚 Poisson Gradient Recovery

**PHYSICS:** heat_transfer
**DIFFICULTY:** basic
**PHYSICS:** heat_transfer
**DIFFICULTY:** basic
**MIGRATED:** From underworld3-documentation/Notebooks

## Description
Expand Down Expand Up @@ -50,8 +50,12 @@
import numpy as np
import sympy


mesh = uw.meshing.UnstructuredSimplexBox(
minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), cellSize=1 / 12, qdegree=3
minCoords=(0.0, 0.0),
maxCoords=(1.0, 1.0),
cellSize=1 / 12,
qdegree=3,
)

mesh.dm.view()
Expand All @@ -60,12 +64,26 @@
# mesh variables

t_soln = uw.discretisation.MeshVariable("T", mesh, 1, degree=3)

dTdY = uw.discretisation.MeshVariable(
r"\partial T/ \partial \mathbf{y}", mesh, 1, degree=2
r"\partial T/ \partial \mathbf{y}",
mesh,
1,
degree=2,
)

kappa = uw.discretisation.MeshVariable(
r"\kappa",
mesh,
1,
degree=2,
)
kappa = uw.discretisation.MeshVariable(r"\kappa", mesh, 1, degree=2)

gradT = uw.discretisation.MeshVariable(
r"\nabla\left[T\right]", mesh, mesh.dim, degree=2
r"\nabla\left[T\right]",
mesh,
mesh.dim,
degree=2,
)


Expand All @@ -86,7 +104,6 @@

poisson = uw.systems.Poisson(mesh, u_Field=t_soln)


poisson.constitutive_model = uw.constitutive_models.DiffusionModel

# Non-linear diffusivity
Expand All @@ -95,21 +112,19 @@
k = 5 + (delT.dot(delT)) / 2

poisson.constitutive_model.Parameters.diffusivity = k
display(poisson.constitutive_model.c)
print(poisson.constitutive_model.c)

# projector for diffusivity (though we can just switch the rhs for the gradient object
# projector for diffusivity, though we can just switch the rhs for the gradient object

# +
diffusivity = uw.systems.Projection(mesh, kappa)
diffusivity.uw_function = sympy.Matrix(
[poisson.constitutive_model.Parameters.diffusivity]
)

diffusivity.add_essential_bc([k], "Bottom")
diffusivity.add_essential_bc([k], "Top" )
diffusivity.add_essential_bc([k], "Top")
diffusivity.add_essential_bc([k], "Right")
diffusivity.add_essential_bc([k], "Left" )
# -
diffusivity.add_essential_bc([k], "Left")


# %%
Expand All @@ -118,8 +133,8 @@
poisson.constitutive_model.Parameters.diffusivity

# %%
display(gradT_projector.uw_function)
display(diffusivity.uw_function)
print(gradT_projector.uw_function)
print(diffusivity.uw_function)

# %%
diffusivity.uw_function
Expand All @@ -130,21 +145,21 @@

abs_r2 = x**2 + y**2
poisson.f = -16 * abs_r2

poisson.add_essential_bc([abs_r2], "Bottom")
poisson.add_essential_bc([abs_r2], "Top" )
poisson.add_essential_bc([abs_r2], "Top")
poisson.add_essential_bc([abs_r2], "Right")
poisson.add_essential_bc([abs_r2], "Left" )
poisson.add_essential_bc([abs_r2], "Left")

# +
# %%
# Linear model - starting guess

poisson.constitutive_model.Parameters.diffusivity = 1
poisson.solve(zero_init_guess=True)
# -

# %%
# Solve time

poisson.constitutive_model.Parameters.diffusivity = k
poisson.solve(zero_init_guess=False)

Expand All @@ -164,7 +179,7 @@
# %%
diffusivity.solve()

# non-linear smoothing term (probably not needed especially at the boundary)
# non-linear smoothing term, probably not needed especially at the boundary

gradient.uw_function = sympy.diff(t_soln.fn, mesh.N.y)
gradient.solve(_force_setup=True)
Expand All @@ -173,61 +188,66 @@
gradT_projector.solve()

# **Check** Construct simple linear function which is solution for
# above config. Exclude boundaries from mesh data.

import numpy as np
# above config. Exclude boundaries from mesh data.

mesh_numerical_soln = uw.function.evaluate(t_soln.sym[0], mesh.X.coords)
# if not np.allclose(mesh_numerical_soln, -1.0, rtol=0.01):
# raise RuntimeError("Unexpected values encountered.")

#

# Validate

from mpi4py import MPI

if MPI.COMM_WORLD.size == 1:

import pyvista as pv
import underworld3.visualisation as vis

pvmesh = vis.mesh_to_pv_mesh(mesh)
pvmesh.point_data["T"] = mesh_numerical_soln
pvmesh.point_data["dTdY"] = vis.scalar_fn_to_pv_points(pvmesh, dTdY.sym)
pvmesh.point_data["dTdY1"] = vis.scalar_fn_to_pv_points(pvmesh, gradT.sym[1])
pvmesh.point_data["dTdX1"] = vis.scalar_fn_to_pv_points(pvmesh, gradT.sym[0])
pvmesh.point_data["kappa"] = vis.scalar_fn_to_pv_points(pvmesh, kappa.sym)
pvmesh.point_data["kappa1"] = vis.scalar_fn_to_pv_points(pvmesh, 5 + gradT.sym[0] ** 2 + gradT.sym[1] ** 2)

pl = pv.Plotter(window_size=(1000, 500), shape=(1, 2))

pl.subplot(0, 0)

pl.add_mesh(
pvmesh,
cmap="coolwarm",
edge_color="Black",
show_edges=True,
scalars="T",
use_transparency=False,
opacity=1,
show_scalar_bar=False)

pl.subplot(0, 1)

pl.add_mesh(
pvmesh,
cmap="coolwarm",
edge_color="Black",
show_edges=True,
scalars="dTdY",
use_transparency=False,
opacity=1,
scalar_bar_args=dict(vertical=False)

)

pl.show(cpos="xy", jupyter_backend="html")
# pl.screenshot(filename="test.png")

# #
try:
import pyvista as pv
import underworld3.visualisation as vis

pvmesh = vis.mesh_to_pv_mesh(mesh)
pvmesh.point_data["T"] = mesh_numerical_soln
pvmesh.point_data["dTdY"] = vis.scalar_fn_to_pv_points(pvmesh, dTdY.sym)
pvmesh.point_data["dTdY1"] = vis.scalar_fn_to_pv_points(pvmesh, gradT.sym[1])
pvmesh.point_data["dTdX1"] = vis.scalar_fn_to_pv_points(pvmesh, gradT.sym[0])
pvmesh.point_data["kappa"] = vis.scalar_fn_to_pv_points(pvmesh, kappa.sym)
pvmesh.point_data["kappa1"] = vis.scalar_fn_to_pv_points(
pvmesh,
5 + gradT.sym[0] ** 2 + gradT.sym[1] ** 2,
)

pl = pv.Plotter(window_size=(1000, 500), shape=(1, 2))

pl.subplot(0, 0)

pl.add_mesh(
pvmesh,
cmap="coolwarm",
edge_color="Black",
show_edges=True,
scalars="T",
use_transparency=False,
opacity=1,
show_scalar_bar=False,
)

pl.subplot(0, 1)

pl.add_mesh(
pvmesh,
cmap="coolwarm",
edge_color="Black",
show_edges=True,
scalars="dTdY",
use_transparency=False,
opacity=1,
scalar_bar_args=dict(vertical=False),
)

pl.show(cpos="xy", jupyter_backend="html")
# pl.screenshot(filename="test.png")

except ImportError as err:
print(f"Skipping PyVista visualisation because an optional dependency is missing: {err}")

except Exception as err:
print(f"Skipping PyVista visualisation because plotting failed: {err}")
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