# update sol.
c0.assign(w.sub(0))
# # acochambramento c (c<1) and (c>0)
# val = c0.dat.data
# if np.any((val > cIn) + (val < np.sqrt(tol))):
# val[val > cIn] = 1.
# val[val < np.sqrt(tol)] = tol
# c0.dat.data[:] = val
# %%
# 5) print results
if it % freq_res == 0 or t == sim_time:
if verbose:
contours = fd.tripcolor(c0)
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.colorbar(contours)
plt.show()
# Computed flux, scalar, and trace
c_h, q_h, lamb = w.split()
c_h.rename("c_h")
q_h.rename("q_h")
# print results
outfile.write(c_h, q_h, time=t)
print('-- write results @ t= {}'.format(t))
print(f'DOF = {W.dim()}')
if verbose:
fd.triplot(mesh)
plt.legend()
plt.savefig("plots/sb_adr_supg_mesh.png")
# Define subdomains
x = fd.SpatialCoordinate(mesh)
logical = fd.And(fd.And(x[0] > Lx * wx, x[1] > Ly * wy),
fd.And(x[0] < Lx * (1 - wx), x[1] < Ly * (1 - wy)))
square = fd.conditional(logical, 1 / k_cavern, 1 / k_porous)
ikm = fd.Function(fd.FunctionSpace(mesh, "DG", 0))
ikm.interpolate(square)
if verbose:
contours = fd.tripcolor(ikm, cmap="viridis")
cbar = plt.colorbar(contours, aspect=10)
cbar.set_label("Porous Domain")
plt.savefig("plots/sb_adr_supg_doamins.png")
# 3) Setting problem (FunctionSpace, Init.Bound.Condition, VariationalForms)
# 3.1) Set Function spaces
V = fd.VectorFunctionSpace(mesh, "CG", order + 1)
P = fd.FunctionSpace(mesh, "CG", order)
# Define function space for system of concentrations (transport)
X = fd.FunctionSpace(mesh, "CG", order)
# Others function space
DG0 = fd.FunctionSpace(mesh, "DG", 0)
def tripcolor(function, *args, **kwargs):
r"""Create a pseudo-color plot of a finite element field"""
return firedrake.tripcolor(_project_to_2d(function), *args, **kwargs)
if verbose:
fd.triplot(mesh)
plt.legend()
plt.savefig("SB_hdiv_mesh.png")
# Define subdomains
x = fd.SpatialCoordinate(mesh)
# domain = fd.And(fd.And(x[0] > Lx*wx, x[1] > Ly*wy),
# fd.And(x[0] < Lx*(1-wx), x[1] < Ly*(1-wy)))
domain = x[1] < Ly * wy
square = fd.conditional(domain, 1 / k_cavern, 1 / k_porous)
ikm = fd.Function(fd.FunctionSpace(mesh, "DG", 0), name='invK')
ikm.interpolate(square)
if verbose:
contours = fd.tripcolor(ikm, shading='flat', cmap="viridis")
cbar = plt.colorbar(contours, aspect=10)
cbar.set_label('Porous Domain')
plt.savefig("plots/SB_hdiv_doamins.png")
# 3) Setting problem (FunctionSpace, Init.Condition, VariationalForms)
# 3.1) Function spaces
if quad_mesh:
RT1 = fd.FunctionSpace(mesh, "RTCF", order)
DG0 = fd.FunctionSpace(mesh, "DQ", order - 1)
else:
RT1 = fd.FunctionSpace(mesh, "RT", order)
DG0 = fd.FunctionSpace(mesh, "DG", order - 1)
# Create mixed function spaces
W = RT1 * DG0
# Setup Plot
ukw = {'vmin': 0.0, 'vmax': +0.2}
kw = {'vmin': -4, 'vmax': +4, 'shading': 'gouraud'}
title_fontsize = 20
text_fontsize = 20
fig, axes = plt.subplots(ncols=3, nrows=1+len(methods), sharex=True, sharey=True, figsize=(20,30), dpi=200)
plt.suptitle('Estimating Log-Conductivity $q$ \n where $k = k_0e^q$ and $-\\nabla \\cdot k \\nabla u = f$ for known $f$', fontsize=title_fontsize)
for ax in axes.ravel():
ax.set_aspect('equal')
# Plot True solution
print('plotting true solution')
# Column 0
axes[0, 0].set_title('$u_{true}$', fontsize=title_fontsize)
colors = firedrake.tripcolor(u_true, axes=axes[0, 0], shading='gouraud', **ukw)
cax = make_axes_locatable(axes[0, 0]).append_axes("right", size="5%", pad=0.05)
fig.colorbar(colors, cax=cax)
# Column 1
axes[0, 1].set_title('$q_{true}$', fontsize=title_fontsize)
colors = firedrake.tripcolor(q_true, axes=axes[0, 1], **kw)
cax = make_axes_locatable(axes[0, 1]).append_axes("right", size="5%", pad=0.05)
fig.colorbar(colors, cax=cax)
# Column 2
axes[0, 2].set_title('$q_{true}-q_{true}$', fontsize=title_fontsize)
zero_func = firedrake.Function(Q).assign(q_true-q_true)
axes[0, 2].text(0.5, 0.5, f'$L^2$ Norm {firedrake.norm(zero_func, "L2"):.2f}', ha='center', fontsize=text_fontsize)
colors = firedrake.tripcolor(zero_func, axes=axes[0, 2], **kw);
cax = make_axes_locatable(axes[0, 2]).append_axes("right", size="5%", pad=0.05)
fig.colorbar(colors, cax=cax)
if verbose:
fd.triplot(mesh)
plt.legend()
plt.savefig("SB_hdiv_mesh.png")
# Define subdomains
x = fd.SpatialCoordinate(mesh)
domain = fd.And(fd.And(x[0] > Lx * wx, x[1] > Ly * wy),
fd.And(x[0] < Lx * (1 - wx), x[1] < Ly * (1 - wy)))
square = fd.conditional(domain, 1 / k_cavern, 1 / k_porous)
ikm = fd.Function(fd.FunctionSpace(mesh, "DG", 0), name='invK')
ikm.interpolate(square)
if verbose:
contours = fd.tripcolor(ikm, shading='flat', cmap="viridis")
cbar = plt.colorbar(contours, aspect=10)
cbar.set_label('Porous Domain')
plt.savefig("plots/SB_hdiv_doamins.png")
# 3) Setting problem (FunctionSpace, Init.Condition, VariationalForms)
# 3.1) Function spaces
if quad_mesh:
RT1 = fd.FunctionSpace(mesh, "RTCF", order)
DG0 = fd.FunctionSpace(mesh, "DQ", order - 1)
else:
RT1 = fd.FunctionSpace(mesh, "RT", order)
DG0 = fd.FunctionSpace(mesh, "DG", order - 1)
# Create mixed function spaces
W = RT1 * DG0
