# <codecell>
from dune.ufl import expression2GF
indicator = expression2GF(gridView,
dot(grad(u_h[0]), grad(u_h[0])),
0,
name="indicator")
# <markdowncell>
# We do the initial refinement of the grid.
# <codecell>
maxLevel = 9
startLevel = 4
hgrid = gridView.hierarchicalGrid
hgrid.globalRefine(startLevel)
for i in range(startLevel, maxLevel):
fem.mark(indicator, 1.4, 1.2, 0, maxLevel)
fem.adapt(u_h)
fem.loadBalance(u_h)
u_h.interpolate(initial_gf)
# <markdowncell>
# Let us start by plotting the initial state of the material, which is just a small circle in the centre.
# <codecell>
from dune.fem.plotting import plotComponents
import matplotlib.pyplot as pyplot
from dune.fem.function import levelFunction, partitionFunction
import matplotlib
vtk = gridView.sequencedVTK(
"crystal",
pointdata=[u_h],
polOrder = space.localOrder(element)
newPolOrder = polOrder
if estP < pTol:
newPolOrder = polOrder - 1 if polOrder > 2 else polOrder
elif estP > 100 * pTol:
newPolOrder = polOrder + 1 if polOrder < maxOrder else polOrder
pMarked[polOrder - 1] += 1
return polOrder
while True:
estimator(solution, estimate)
eta2 = sum(estimate.dofVector)
vtk()
print("estimate:", eta2, tolerance)
if eta2 < tolerance * tolerance * 2:
break
hMarked = mark(estimate, math.sqrt(eta2) / grid.size(0))
# globalRefine(1,solution,solution)
adapt(solution)
print("h-adapted:", hMarked)
estimator(solution, estimate)
spaceAdapt(spacePm, markPm, [solutionPm])
solutionPm.interpolate(solution)
estimator(solutionPm, estimatePm)
spaceAdapt(space, markp, [solution])
print("p-adapted:", pMarked)
scheme.solve(target=solution)
plot(uh, figure=(fig, 131 + count // 9), colorbar=False)
pointFunctional.clear()
error = computeFunctional(point, pointFunctional, eh)
dual.solve(target=z, rhs=pointFunctional)
zh.interpolate(z)
estimator(uh, estimate)
eta = sum(estimate.dofVector)
dofs += [uh.space.size]
errorVector += [error]
estimateVector += [eta]
if count % 3 == 2:
print(count, ": size=", uh.space.grid.size(0), "estimate=", eta,
"error=", error)
if eta < tolerance:
break
marked = fem.mark(estimate, eta / uh.space.grid.size(0))
fem.adapt(
uh) # can also be a list or tuple of function to prolong/restrict
fem.loadBalance(uh)
count += 1
plot(uh, figure=(fig, 131 + 2), colorbar=False)
pyplot.show()
pyplot.close('all')
# <markdowncell>
# Let's take a close up look of the refined region around the point of
# interest and the origin:
# <codecell>
fig = pyplot.figure(figsize=(30, 20))
plot(uh,
# <codecell>
from dune.ufl import expression2GF
indicator = expression2GF(gridView,
dot(grad(u_h[0]), grad(u_h[0])),
0,
name="indicator")
# <markdowncell>
# We do the initial refinement of the grid.
# <codecell>
maxLevel = 8
startLevel = 3
gridView.hierarchicalGrid.globalRefine(startLevel)
u_h.interpolate(initial_gf)
for i in range(startLevel, maxLevel):
marked = fem.mark(indicator, 1.4, 1.2, 0, maxLevel)
# print("marked:",marked,"from elements",gridView.size(0))
fem.adapt(gridView.hierarchicalGrid)
fem.loadBalance(gridView.hierarchicalGrid)
# print(gridView.size(0), end="\n")
u_h.interpolate(initial_gf)
# print()
# <markdowncell>
# Let us start by plotting the initial state of the material, which is just a small circle in the centre.
# <codecell>
from dune.fem.plotting import plotComponents
import matplotlib.pyplot as pyplot
from dune.fem.function import levelFunction, partitionFunction
import matplotlib