def test_failsafe_sweep():
interpolate_expression = Expression('x[0]', degree=1)
mesh = UnitSquareMesh(5, 5)
V = FunctionSpace(mesh, "DG", 1)
v = Function(V)
v.assign(interpolate_expression)
np_min, np_max = 1, 2
np_failsafe = 4
# Initialize particles
x = RandomRectangle(Point(0.0, 0.0), Point(1., 1.)).generate([100, 100])
s = assign_particle_values(x, interpolate_expression)
# Broadcast to other procs
x = comm.bcast(x, root=0)
s = comm.bcast(s, root=0)
property_idx = 1
p = particles(x, [s], mesh)
AD = AddDelete(p, np_min, np_max, [v])
AD.do_sweep_failsafe(np_failsafe)
# Must recover linear
lstsq_rho = l2projection(p, V, property_idx)
lstsq_rho.project(v.cpp_object())
error = sqrt(
assemble(
(v - interpolate_expression) * (v - interpolate_expression) * dx))
assert len(p.positions() == mesh.num_cells() * np_failsafe)
assert error < 1e-12
def test_l2_projection_3D(polynomial_order, in_expression):
xmin, ymin, zmin = 0.0, 0.0, 0.0
xmax, ymax, zmax = 1.0, 1.0, 1.0
nx = 25
property_idx = 1
mesh = BoxMesh(Point(xmin, ymin, zmin), Point(xmax, ymax, zmax), nx, nx,
nx)
interpolate_expression = Expression(in_expression, degree=3)
if len(interpolate_expression.ufl_shape) == 0:
V = FunctionSpace(mesh, "DG", polynomial_order)
elif len(interpolate_expression.ufl_shape) == 1:
V = VectorFunctionSpace(mesh, "DG", polynomial_order)
v_exact = Function(V)
v_exact.assign(interpolate_expression)
x = RandomBox(Point(0.0, 0.0, 0.0), Point(1.0, 1.0,
1.0)).generate([4, 4, 4])
s = assign_particle_values(x, interpolate_expression)
# Just make a complicated particle, possibly with scalars and vectors mixed
p = particles(x, [s], mesh)
# Do AddDelete sweep
AD = AddDelete(p, 13, 15, [v_exact])
AD.do_sweep()
vh = Function(V)
lstsq_vh = l2projection(p, V, property_idx)
lstsq_vh.project(vh.cpp_object())
error_sq = abs(assemble(dot(v_exact - vh, v_exact - vh) * dx))
if comm.Get_rank() == 0:
assert error_sq < 1e-13
forms_pde["Q_a"],
forms_pde["R_a"],
forms_pde["S_a"],
[bc],
property_idx,
)
# Initialize the l2 projection
lstsq_psi = l2projection(p, W, property_idx)
# Set initial condition at mesh and particles
psi0_h.interpolate(psi0_expression)
p.interpolate(psi0_h.cpp_object(), property_idx)
# Initialize add/delete particle
AD = AddDelete(p, 15, 25, [psi0_h])
step = 0
t = 0.0
area_0 = assemble(psi0_h * dx)
timer = Timer()
timer.start()
while step < num_steps:
step += 1
t += float(dt)
if comm.rank == 0:
print("Step " + str(step))
# Advect particle, assemble and solve pde projection
Vcg = FunctionSpace(model.mesh.mesh, 'DG', 1)
(xp, pstrain, ptemp,
pepsII) = (p.return_property(mesh, 0), p.return_property(mesh, 1),
p.return_property(mesh, 2), p.return_property(mesh, 3))
del p
p = particles(xp, [pstrain, ptemp, pepsII], model.mesh.mesh)
else:
p.relocate()
# Advect particles -- Turn this on to advect particles now that it is removed from Stokes script
Vdg = FunctionSpace(model.mesh.mesh, 'DG', 1)
ap = advect_rk3(p, model.vector2, model.u_k, "open")
ap.do_step(time_step)
AD = AddDelete(p, p_min, p_max, [
interpolate(model.strain, Vdg),
interpolate(model.temp, Vdg),
interpolate(model.epsII, Vdg)
]) # Sweep over mesh to delete/insert particles
AD.do_sweep()
# Plotting
(xp, pstrain, ptemp,
pepsII) = (p.return_property(mesh, 0), p.return_property(mesh, 1),
p.return_property(mesh, 2), p.return_property(mesh, 3))
pstrain[xp[:, 0] < xyield_min] = 0.0
p.change_property(pstrain, 1)
xx = np.linspace(0, length * 1.5, 101)
xs = np.linspace(0, length, 101)
plt.figure(1)
forms_pde["L_a"],
forms_pde["H_a"],
forms_pde["B_a"],
forms_pde["Q_a"],
forms_pde["R_a"],
forms_pde["S_a"],
[],
property_idx,
)
# Set initial condition at mesh and particles
psi0_h.interpolate(psi0_expression)
p.interpolate(psi0_h.cpp_object(), property_idx)
# Add/Delete particles
AD = AddDelete(p, 10, 20, [psi0_h])
step = 0
area_0 = assemble(psi0_h * dx)
timer = Timer()
timer.start()
while step < num_steps:
step += 1
# Add/delete particles, must be done before advection!
AD.do_sweep()
# Advect particle, assemble and solve pde projection
ap.do_step(float(dt))
pde_projection.assemble(True, True)
uh = Function(V)
uh.assign(Expression(('-Uh*x[1]', 'Uh*x[0]'), Uh=Uh, degree=3))
# Generate particles
x = RandomCircle(Point(x0, y0), r).generate([pres, pres])
s = assign_particle_values(x, psi0_expr)
p = particles(x, [s], mesh)
# Initialize advection class, use RK3 scheme
ap = advect_rk3(p, V, uh, 'closed')
# Init projection
lstsq_psi = l2projection(p, W, 1)
# Do projection to get initial field
lstsq_psi.project(psi_h.cpp_object(), lb, ub)
AD = AddDelete(p, 10, 20, [psi_h], [1], [lb, ub])
step = 0
t = 0.
area_0 = assemble(psi_h * dx)
timer = Timer()
timer.start()
outfile.write(psi_h, t)
while step < num_steps:
step += 1
t += float(dt)
if comm.Get_rank() == 0:
print("Step " + str(step))
# Define the variational (projection problem)
k = 1
W_e = FiniteElement("DG", mesh.ufl_cell(), k)
T_e = FiniteElement("DG", mesh.ufl_cell(), 0)
Wbar_e = FiniteElement("DGT", mesh.ufl_cell(), k)
# Composition field space
Wh = FunctionSpace(mesh, W_e)
Th = FunctionSpace(mesh, T_e)
Wbarh = FunctionSpace(mesh, Wbar_e)
phi = interpolate(StepFunction(), Wh)
gamma0 = interpolate(StepFunction(), Wh)
ad = AddDelete(ptcls, 50, 55, [phi], [1], [0.0, 1.0])
ptcls.interpolate(phi, property_idx)
ad.do_sweep()
lambda_h = Function(Th)
psibar_h = Function(Wbarh)
# Elements for Stokes
W_e_2 = VectorElement("DG", mesh.ufl_cell(), k)
T_e_2 = VectorElement("DG", mesh.ufl_cell(), 0)
Wbar_e_2 = VectorElement("DGT", mesh.ufl_cell(), k)
Wbar_e_2_H12 = VectorElement("CG", mesh.ufl_cell(), k)["facet"]
Q_E = FiniteElement("DG", mesh.ufl_cell(), k-1)
Qbar_E = FiniteElement("DGT", mesh.ufl_cell(), k)
# Define the variational (projection problem)
k = 1
W_e = FiniteElement("DG", mesh.ufl_cell(), k)
T_e = FiniteElement("DG", mesh.ufl_cell(), 0)
Wbar_e = FiniteElement("DGT", mesh.ufl_cell(), k)
# Composition field space
Wh = FunctionSpace(mesh, W_e)
Th = FunctionSpace(mesh, T_e)
Wbarh = FunctionSpace(mesh, Wbar_e)
phi = interpolate(StepFunction(), Wh)
gamma0 = interpolate(StepFunction(), Wh)
ad = AddDelete(ptcls, 25, 30, [phi], [1], [0.0, 1.0])
ptcls.interpolate(phi, property_idx)
ad.do_sweep()
lambda_h = Function(Th)
psibar_h = Function(Wbarh)
# Elements for Stokes
W_e_2 = VectorElement("DG", mesh.ufl_cell(), k)
T_e_2 = VectorElement("DG", mesh.ufl_cell(), 0)
Wbar_e_2 = VectorElement("DGT", mesh.ufl_cell(), k)
Wbar_e_2_H12 = VectorElement("CG", mesh.ufl_cell(), k)["facet"]
Q_E = FiniteElement("DG", mesh.ufl_cell(), k - 1)
Qbar_E = FiniteElement("DGT", mesh.ufl_cell(), k)
lims = np.array([
[xmin, xmin, ymin, ymax],
[xmax, xmax, ymin, ymax],
[xmin, xmax, ymin, ymin],
[xmin, xmax, ymax, ymax],
])
# Particle specific momentum is stored at slot 1
# the second slot will be to store old velocities at particle level
property_idx = 1
p = particles(x, [s, s], mesh)
ap = advect_rk3(p, W_2, Udiv, "periodic", lims.flatten())
# Particle management
AD = AddDelete(p, 10, 20, [Udiv, duh0])
# Forms PDE map
funcspace_dict = {
"FuncSpace_local": W_2,
"FuncSpace_lambda": T_2,
"FuncSpace_bar": Wbar_2
}
forms_adv = FormsPDEMap(mesh, funcspace_dict).forms_theta_nlinear(
u0_a,
ubar0_a,
dt,
theta_map=Constant(1.0),
theta_L=theta_L,
duh0=duh0,
duh00=duh00)
[xmin, xmin, ymin, ymax, zmin, zmax],
[xmax, xmax, ymin, ymax, zmin, zmax],
[xmin, xmax, ymin, ymin, zmin, zmax],
[xmin, xmax, ymax, ymax, zmin, zmax],
[xmin, xmax, ymin, ymax, zmin, zmin],
[xmin, xmax, ymin, ymax, zmax, zmax],
])
# Particle specific momentum is stored at slot 1
# the second slot will be to store old velocities at particle level
property_idx = 1
p = particles(x, [s, s], mesh)
ap = advect_rk3(p, W_2, Udiv, "periodic", lims.flatten())
# Particle management
AD = AddDelete(p, 15, 25, [Udiv, duh0])
# Forms PDE map
funcspace_dict = {
"FuncSpace_local": W_2,
"FuncSpace_lambda": T_2,
"FuncSpace_bar": Wbar_2
}
forms_adv = FormsPDEMap(mesh, funcspace_dict).forms_theta_nlinear(
u0_a,
ubar0_a,
dt,
theta_map=Constant(1.0),
theta_L=theta_L,
duh0=duh0,
duh00=duh00)
