'''
Domain mapping perturbation
'''
number_of_channels = len(CoefClass.ShapeRemember)
bending_perturbation = perturbations.MultipleMovingStripes(world, number_of_channels, space, thick, plot_mapping = True)
aFine_pert, f_pert = bending_perturbation.computePerturbation(aFine_with_defects, f_ref)
aFine_trans, f_trans = bending_perturbation.computeTransformation(aFine_with_defects, f_ref)
'''
Plot diffusion coefficient and right hand side
'''
plt.figure("Coefficient")
drawCoefficient_origin(NFine, aFine_ref)
plt.figure("Perturbed coefficient")
drawCoefficient_origin(NFine, aFine_pert)
plt.figure('transformed')
drawCoefficient_origin(NFine, aFine_trans)
plt.figure('Right hand side')
draw_f(NFine+1, f_ref)
plt.show()
'''
Check whether domain mapping method works sufficiently good
'''
plot data
'''
plt.figure("Coefficient")
if ROOT == "ex2_noisy":
lim = [np.max(a_trans), np.min(a_trans)] # for ex2
elif ROOT == "ex3_noisy":
lim = [np.max(a_trans), np.min(a_ref)] # for ex3
elif ROOT == "ex2":
lim = [np.max(a_trans), np.min(a_trans)] # for ex2
elif ROOT == "ex3":
lim = [np.max(a_trans), np.min(a_ref)] # for ex3
else:
lim = None
drawCoefficient_origin(NFine, a_ref, lim=lim)
if extract_figures_to_files:
for fmt in FIGURE_OUTPUTS:
plt.savefig("tikz/{}_{}_original.{}".format(ROOT, name, fmt),
bbox_inches='tight',
dpi=dpi)
plt.figure("Perturbed coefficient")
drawCoefficient_origin(NFine, a_pert, lim=lim)
if extract_figures_to_files:
for fmt in FIGURE_OUTPUTS:
plt.savefig("tikz/{}_{}_perturbed.{}".format(ROOT, name, fmt),
bbox_inches='tight',
dpi=dpi)
plt.figure('transformed')
Construct diffusion coefficient
'''
space = 3 * factor
thick = 6 * factor
bg = 0.1 #background
val = 1 #values
soilinput = np.array([[8, 6, 3], [8, 3, 6], [10, 3, 4]])
soilMatrix = buildcoef2d.soil_converter(soilinput, NFine, BoundarySpace=space)
print(soilMatrix)
CoefClass = buildcoef2d.Coefficient2d(NFine,
bg=bg,
val=val,
length=thick,
thick=thick,
space=space,
probfactor=1,
right=1,
equidistant=True,
BoundarySpace=True,
soilMatrix=soilMatrix)
aFine = CoefClass.BuildCoefficient().flatten()
plt.figure("Coefficient")
drawCoefficient_origin(NFine, aFine)
plt.show()
# Set reference coefficient
aCoarse_ref_shaped = CoefClass.BuildCoefficient()
aCoarse_ref = aCoarse_ref_shaped.flatten()
aFine_ref = func.evaluateDQ0(NCoeff, aCoarse_ref, xtFine_ref)
# Compute perturbed coefficient
# Coefficient and right hand side naming:
# ._pert is a function defined on the uniform grid in the perturbed domain
# ._ref is a function defined on the uniform grid in the reference domain
# ._trans is a function defined on the uniform grid on the reference domain,
# after transformation from the perturbed domain
aFine_pert = func.evaluateDQ0(NFine, aFine_ref, xtFine_ref)
aBack_ref = func.evaluateDQ0(NFine, aFine_pert, xtFine_pert)
plt.figure("Coefficient")
drawCoefficient_origin(NFine, aFine_ref)
plt.figure("a_perturbed")
drawCoefficient_origin(NFine, aFine_pert)
plt.figure("a_back")
drawCoefficient_origin(NFine, aBack_ref)
# aFine_trans is the transformed perturbed reference coefficient
aFine_trans = np.einsum('tji, t, tkj, t -> tik', psi.Jinv(xtFine), aFine_ref, psi.Jinv(xtFine), psi.detJ(xtFine))
f_pert = np.ones(np.prod(NFine+1))
f_ref = func.evaluateCQ1(NFine, f_pert, xpFine_pert)
f_trans = np.einsum('t, t -> t', f_ref, psi.detJ(xpFine))
#d3sol(NFine,f, 'right hand side NT')