def test_mesh_metric3D():
mesh = BoxMesh(0, 0, 0, 1, 1, 1, 20, 20, 20)
mesh = adapt(
interpolate(Constant(((100., 0., 0.), (0., 100., 0.), (0., 0., 100.))),
TensorFunctionSpace(mesh, 'CG', 1)))
#extract mesh metric
MpH = mesh_metric2(mesh)
for i in range(0, 40):
thecell = mesh.cells()[i]
ind = MpH.function_space().dofmap().cell_dofs(i)
coords = mesh.coordinates()[thecell, :]
r1 = coords[1, :] - coords[0, :]
r2 = coords[2, :] - coords[0, :]
r3 = coords[0:3, :].mean(0) - coords[3, :]
r12c = cross(r2, r1) / 6.
det1234 = pyabs((r12c * r3).sum())
H = MpH.vector().gather(ind).reshape(
3, 3) # H = array([[H[1],H[0]],[H[0],H[2]]])
[v, w] = linalg.eig(H)
print(
'tetrahedron volume: %0.6f, ellipsoid axis product(*sqrt(2)/12): %0.6f'
% (det1234, v.prod() * sqrt(2) / 12))
print v.prod() * sqrt(2) / 12 / (det1234)
def test_mesh_metric():
mesh = RectangleMesh(0, 0, 1, 1, 20, 20)
mesh = adapt(
interpolate(Constant(((10., 0.), (0., 10.))),
TensorFunctionSpace(mesh, 'CG', 1)))
#extract mesh metric
MpH = mesh_metric2(mesh)
# Plot element i
i = 20
t = linspace(0, 2 * pi, 101)
ind = MpH.function_space().dofmap().cell_dofs(i)
thecell = mesh.cells()[i]
centerxy = mesh.coordinates()[thecell, :].mean(0).repeat(3).reshape([2,
3]).T
cxy = mesh.coordinates()[thecell, :] - centerxy
pyplot(cxy[:, 0], cxy[:, 1], '-b')
H = MpH.vector().gather(ind).reshape(2, 2)
# H = array([[H[1],H[0]],[H[0],H[2]]])
#H = MpH.vector().gather(ind); H = array([[H[1],H[0]],[H[0],H[2]]])
#H = MpH.vector().array()[ind]; H = array([[H[1],H[0]],[H[0],H[2]]])
[v, w] = linalg.eig(H)
v /= pysqrt(3) #v = 1/pysqrt(v)/pysqrt(3)
elxy = array([pycos(t), pysin(t)]).T.dot(w).dot(diag(v)).dot(w.T)
hold('on')
pyplot(elxy[:, 0], elxy[:, 1], '-r')
hold('off')
axis('equal')
print('triangle area: %0.6f, ellipse axis product(*3*sqrt(3)/4): %0.6f' % (
pyabs(linalg.det(array([cxy[1, :] - cxy[0, :], cxy[2, :] - cxy[0, :]
]))) / 2, v[0] * v[1] * 3 * sqrt(3) / 4))
show()
def test_mesh_metric3D():
mesh = BoxMesh(0,0,0,1,1,1,20,20,20)
mesh = adapt(interpolate(Constant(((100.,0.,0.),(0.,100.,0.),(0.,0.,100.))),TensorFunctionSpace(mesh,'CG',1)))
#extract mesh metric
MpH = mesh_metric2(mesh)
for i in range(0,40):
thecell = mesh.cells()[i]
ind = MpH.function_space().dofmap().cell_dofs(i)
coords = mesh.coordinates()[thecell,:]
r1 = coords[1,:]-coords[0,:]
r2 = coords[2,:]-coords[0,:]
r3 = coords[0:3,:].mean(0)-coords[3,:]
r12c = cross(r2,r1)/6.
det1234 = pyabs((r12c*r3).sum())
H = MpH.vector().gather(ind).reshape(3,3)# H = array([[H[1],H[0]],[H[0],H[2]]])
[v,w] = linalg.eig(H)
print('tetrahedron volume: %0.6f, ellipsoid axis product(*sqrt(2)/12): %0.6f' % (det1234,v.prod()*sqrt(2)/12))
print v.prod()*sqrt(2)/12/(det1234)
def test_mesh_metric():
mesh = RectangleMesh(0,0,1,1,20,20)
mesh = adapt(interpolate(Constant(((10.,0.),(0.,10.))),TensorFunctionSpace(mesh,'CG',1)))
#extract mesh metric
MpH = mesh_metric2(mesh)
# Plot element i
i = 20; t = linspace(0,2*pi,101)
ind = MpH.function_space().dofmap().cell_dofs(i)
thecell = mesh.cells()[i]
centerxy = mesh.coordinates()[thecell,:].mean(0).repeat(3).reshape([2,3]).T
cxy = mesh.coordinates()[thecell,:]-centerxy
pyplot(cxy[:,0],cxy[:,1],'-b')
H = MpH.vector().gather(ind).reshape(2,2);# H = array([[H[1],H[0]],[H[0],H[2]]])
#H = MpH.vector().gather(ind); H = array([[H[1],H[0]],[H[0],H[2]]])
#H = MpH.vector().array()[ind]; H = array([[H[1],H[0]],[H[0],H[2]]])
[v,w] = linalg.eig(H); v /= pysqrt(3) #v = 1/pysqrt(v)/pysqrt(3)
elxy = array([pycos(t),pysin(t)]).T.dot(w).dot(diag(v)).dot(w.T)
hold('on'); pyplot(elxy[:,0],elxy[:,1],'-r'); hold('off'); axis('equal')
print('triangle area: %0.6f, ellipse axis product(*3*sqrt(3)/4): %0.6f' % (pyabs(linalg.det(array([cxy[1,:]-cxy[0,:],cxy[2,:]-cxy[0,:]])))/2,v[0]*v[1]*3*sqrt(3)/4))
show()
def adv_convergence(width=2e-2,
delta=1e-2,
relp=1,
Nadapt=10,
use_adapt=True,
problem=3,
outname='',
use_reform=False,
CGorderL=[2, 3],
noplot=False,
Lx=3.):
### SETUP SOLUTION
sy = Symbol('sy')
width_ = Symbol('ww')
if problem == 3:
stepfunc = 0.5 + 165. / 104. / width_ * sy - 20. / 13. / width_**3 * sy**3 - 102. / 13. / width_**5 * sy**5 + 240. / 13. / width_**7 * sy**7
elif problem == 2:
stepfunc = 0.5 + 15. / 8. / width_ * sy - 5. / width_**3 * sy**3 + 6. / width_**5 * sy**5
elif problem == 1:
stepfunc = 0.5 + 1.5 / width_ * sy - 2 / width_**3 * sy**3
stepfunc = str(stepfunc).replace('sy',
'x[1]').replace('x[1]**2', '(x[1]*x[1])')
#REPLACE ** with pow
stepfunc = stepfunc.replace('x[1]**3', 'pow(x[1],3.)')
stepfunc = stepfunc.replace('x[1]**5', 'pow(x[1],5.)')
stepfunc = stepfunc.replace('x[1]**7', 'pow(x[1],7.)')
testsol = '(-ww/2 < x[1] && x[1] < ww/2 ? ' + stepfunc + ' : 0) + (ww/2<x[1] ? 1 : 0)'
testsol = testsol.replace('ww**2', '(ww*ww)').replace(
'ww**3',
'pow(ww,3.)').replace('ww**5',
'pow(ww,5.)').replace('ww**7', 'pow(ww,7.)')
testsol = testsol.replace('ww', str(width))
dp = Constant(1.)
fac = Constant(1 + 2. * delta)
delta = Constant(delta)
def left(x, on_boundary):
return x[0] + Lx / 2. < DOLFIN_EPS
def right(x, on_boundary):
return x[0] - Lx / 2. > -DOLFIN_EPS
def top_bottom(x, on_boundary):
return x[1] - 0.5 > -DOLFIN_EPS or x[1] + 0.5 < DOLFIN_EPS
class Inletbnd(SubDomain):
def inside(self, x, on_boundary):
return x[0] + Lx / 2. < DOLFIN_EPS
for CGorder in [2]: #CGorderL:
dofs = []
L2errors = []
for eta in 0.04 * pyexp2(-array(range(9)) * pylog(2) / 2):
### SETUP MESH
meshsz = int(
round(80 * 0.005 / (eta * (bool(use_adapt) == False) + 0.05 *
(bool(use_adapt) == True))))
if not bool(use_adapt) and meshsz > 80:
continue
mesh = RectangleMesh(-Lx / 2., -0.5, Lx / 2., 0.5, meshsz, meshsz,
"left/right")
# PERFORM TEN ADAPTATION ITERATIONS
for iii in range(Nadapt):
V = VectorFunctionSpace(mesh, "CG", CGorder)
Q = FunctionSpace(mesh, "CG", CGorder - 1)
W = V * Q
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
alpha = Expression(
"-0.25<x[0] && x[0]<0.25 && 0. < x[1] ? 1e4 : 0")
boundaries = FacetFunction("size_t", mesh)
#outletbnd = Outletbnd()
inletbnd = Inletbnd()
boundaries.set_all(0)
#outletbnd.mark(boundaries, 1)
inletbnd.mark(boundaries, 1)
ds = Measure("ds")[boundaries]
bc0 = DirichletBC(W.sub(0), Constant((0., 0.)), top_bottom)
bc1 = DirichletBC(W.sub(1), dp, left)
bc2 = DirichletBC(W.sub(1), Constant(0), right)
bc3 = DirichletBC(W.sub(0).sub(1), Constant(0.), left)
bc4 = DirichletBC(W.sub(0).sub(1), Constant(0.), right)
bcs = [bc0, bc1, bc2, bc3, bc4]
bndterm = dp * dot(v, Constant((-1., 0.))) * ds(1)
a = eta * inner(grad(u), grad(
v)) * dx - div(v) * p * dx + q * div(u) * dx + alpha * dot(
u, v) * dx #+bndterm
L = inner(Constant((0., 0.)), v) * dx - bndterm
U = Function(W)
solve(a == L, U, bcs)
u, ps = U.split()
#SOLVE CONCENTRATION
mm = mesh_metric2(mesh)
vdir = u / sqrt(inner(u, u) + DOLFIN_EPS)
if iii == 0 or use_reform == False:
Q2 = FunctionSpace(mesh, 'CG', 2)
c = Function(Q2)
q = TestFunction(Q2)
p = TrialFunction(Q2)
newq = (q + dot(vdir, dot(mm, vdir)) * inner(grad(q), vdir)
) #SUPG
if use_reform:
F = newq * (fac / (
(1 + exp(-c))**2) * exp(-c)) * inner(grad(c), u) * dx
J = derivative(F, c)
bc = DirichletBC(
Q2,
Expression("-log(" + str(float(fac)) + "/(" + testsol +
"+" + str(float(delta)) + ")-1)"), left)
# bc = DirichletBC(Q, -ln(fac/(Expression(testsol)+delta)-1), left)
problem = NonlinearVariationalProblem(F, c, bc, J)
solver = NonlinearVariationalSolver(problem)
solver.parameters["newton_solver"][
"relaxation_parameter"] = relp
solver.solve()
else:
a2 = newq * inner(grad(p), u) * dx
bc = DirichletBC(Q2, Expression(testsol), left)
L2 = Constant(0.) * q * dx
solve(a2 == L2, c, bc)
if (not bool(use_adapt)) or iii == Nadapt - 1:
break
um = project(sqrt(inner(u, u)), FunctionSpace(mesh, 'CG', 2))
H = metric_pnorm(um,
eta,
max_edge_ratio=1 + 49 * (use_adapt != 2),
p=2)
H2 = metric_pnorm(c,
eta,
max_edge_ratio=1 + 49 * (use_adapt != 2),
p=2)
#H3 = metric_pnorm(ps , eta, max_edge_ratio=1+49*(use_adapt!=2), p=2)
H4 = metric_ellipse(H, H2)
#H5 = metric_ellipse(H3,H4,mesh)
mesh = adapt(H4)
if use_reform:
Q2 = FunctionSpace(mesh, 'CG', 2)
c = interpolate(c, Q2)
if use_reform:
c = project(fac / (1 + exp(-c)) - delta,
FunctionSpace(mesh, 'CG', 2))
L2error = bnderror(c, Expression(testsol), ds)
dofs.append(len(c.vector().array()) + len(U.vector().array()))
L2errors.append(L2error)
# fid = open("DOFS_L2errors_mesh_c_CG"+str(CGorder)+outname+".mpy",'w')
# pickle.dump([dofs[0],L2errors[0],c.vector().array().min(),c.vector().array().max()-1,mesh.cells(),mesh.coordinates(),c.vector().array()],fid)
# fid.close();
log(
INFO + 1,
"%1dX ADAPT<->SOLVE complete: DOF=%5d, error=%0.0e, min(c)=%0.0e,max(c)-1=%0.0e"
% (Nadapt, dofs[len(dofs) - 1], L2error,
c.vector().array().min(), c.vector().array().max() - 1))
# PLOT MESH + solution
figure()
testf = interpolate(c, FunctionSpace(mesh, 'CG', 1))
testfe = interpolate(Expression(testsol), FunctionSpace(mesh, 'CG', 1))
vtx2dof = vertex_to_dof_map(FunctionSpace(mesh, "CG", 1))
zz = testf.vector().array()[vtx2dof]
zz[zz == 1] -= 1e-16
hh = tricontourf(mesh.coordinates()[:, 0],
mesh.coordinates()[:, 1],
mesh.cells(),
zz,
100,
cmap=get_cmap('binary'))
colorbar(hh)
hold('on')
triplot(mesh.coordinates()[:, 0],
mesh.coordinates()[:, 1],
mesh.cells(),
color='r',
linewidth=0.5)
hold('off')
axis('equal')
box('off')
# savefig(outname+'final_mesh_CG2.png',dpi=300) #; savefig('outname+final_mesh_CG2.eps',dpi=300)
#PLOT ERROR
figure()
xe = interpolate(Expression("x[0]"),
FunctionSpace(mesh, 'CG', 1)).vector().array()
ye = interpolate(Expression("x[1]"),
FunctionSpace(mesh, 'CG', 1)).vector().array()
I = xe - Lx / 2 > -DOLFIN_EPS
I2 = ye[I].argsort()
pyplot(ye[I][I2],
testf.vector().array()[I][I2] - testfe.vector().array()[I][I2],
'-b')
ylabel('error')
# PLOT L2error graph
figure()
pyloglog(dofs, L2errors, '-b.', linewidth=2, markersize=16)
xlabel('Degree of freedoms')
ylabel('L2 error')
# SAVE SOLUTION
dofs = array(dofs)
L2errors = array(L2errors)
fid = open("DOFS_L2errors_CG" + str(CGorder) + outname + ".mpy", 'w')
pickle.dump([dofs, L2errors], fid)
fid.close()
# #show()
# #LOAD SAVED SOLUTIONS
# fid = open("DOFS_L2errors_CG2"+outname+".mpy",'r')
# [dofs,L2errors] = pickle.load(fid)
# fid.close()
#
# PERFORM FITS ON LAST THREE POINTS
NfitP = 5
I = array(range(len(dofs) - NfitP, len(dofs)))
slope, ints = polyfit(pylog(dofs[I]), pylog(L2errors[I]), 1)
fid = open("DOFS_L2errors_CG2_fit" + outname + ".mpy", 'w')
pickle.dump([dofs, L2errors, slope, ints], fid)
fid.close()
#PLOT THEM TOGETHER
if CGorderL != [2]:
fid = open("DOFS_L2errors_CG3.mpy", 'r')
[dofs_old, L2errors_old] = pickle.load(fid)
fid.close()
slope2, ints2 = polyfit(pylog(dofs_old[I]), pylog(L2errors_old[I]), 1)
figure()
pyloglog(dofs,
L2errors,
'-b.',
dofs_old,
L2errors_old,
'--b.',
linewidth=2,
markersize=16)
hold('on')
pyloglog(dofs,
pyexp2(ints) * dofs**slope,
'-r',
dofs_old,
pyexp2(ints2) * dofs_old**slope2,
'--r',
linewidth=1)
hold('off')
xlabel('Degree of freedoms')
ylabel('L2 error')
legend([
'CG2', 'CG3',
"%0.2f*log(DOFs)" % slope,
"%0.2f*log(DOFs)" % slope2
]) #legend(['new data','old_data'])
# savefig('comparison.png',dpi=300) #savefig('comparison.eps');
if not noplot:
show()
def adv_convergence(width=2e-2, delta=1e-2, relp=1, Nadapt=10, use_adapt=True, problem=3, outname='', use_reform=False, CGorderL = [2, 3], noplot=False, Lx=3.):
### SETUP SOLUTION
sy = Symbol('sy'); width_ = Symbol('ww')
if problem == 3:
stepfunc = 0.5+165./104./width_*sy-20./13./width_**3*sy**3-102./13./width_**5*sy**5+240./13./width_**7*sy**7
elif problem == 2:
stepfunc = 0.5+15./8./width_*sy-5./width_**3*sy**3+6./width_**5*sy**5
elif problem == 1:
stepfunc = 0.5+1.5/width_*sy-2/width_**3*sy**3
stepfunc = str(stepfunc).replace('sy','x[1]').replace('x[1]**2','(x[1]*x[1])')
#REPLACE ** with pow
stepfunc = stepfunc.replace('x[1]**3','pow(x[1],3.)')
stepfunc = stepfunc.replace('x[1]**5','pow(x[1],5.)')
stepfunc = stepfunc.replace('x[1]**7','pow(x[1],7.)')
testsol = '(-ww/2 < x[1] && x[1] < ww/2 ? ' + stepfunc +' : 0) + (ww/2<x[1] ? 1 : 0)'
testsol = testsol.replace('ww**2','(ww*ww)').replace('ww**3','pow(ww,3.)').replace('ww**5','pow(ww,5.)').replace('ww**7','pow(ww,7.)')
testsol = testsol.replace('ww',str(width))
dp = Constant(1.)
fac = Constant(1+2.*delta)
delta = Constant(delta)
def left(x, on_boundary):
return x[0] + Lx/2. < DOLFIN_EPS
def right(x, on_boundary):
return x[0] - Lx/2. > -DOLFIN_EPS
def top_bottom(x, on_boundary):
return x[1] - 0.5 > -DOLFIN_EPS or x[1] + 0.5 < DOLFIN_EPS
class Inletbnd(SubDomain):
def inside(self, x, on_boundary):
return x[0] + Lx/2. < DOLFIN_EPS
for CGorder in [2]: #CGorderL:
dofs = []
L2errors = []
for eta in 0.04*pyexp2(-array(range(9))*pylog(2)/2):
### SETUP MESH
meshsz = int(round(80*0.005/(eta*(bool(use_adapt)==False)+0.05*(bool(use_adapt)==True))))
if not bool(use_adapt) and meshsz > 80:
continue
mesh = RectangleMesh(-Lx/2.,-0.5,Lx/2.,0.5,meshsz,meshsz,"left/right")
# PERFORM TEN ADAPTATION ITERATIONS
for iii in range(Nadapt):
V = VectorFunctionSpace(mesh, "CG", CGorder); Q = FunctionSpace(mesh, "CG", CGorder-1)
W = V*Q
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
alpha = Expression("-0.25<x[0] && x[0]<0.25 && 0. < x[1] ? 1e4 : 0")
boundaries = FacetFunction("size_t",mesh)
#outletbnd = Outletbnd()
inletbnd = Inletbnd()
boundaries.set_all(0)
#outletbnd.mark(boundaries, 1)
inletbnd.mark(boundaries, 1)
ds = Measure("ds")[boundaries]
bc0 = DirichletBC(W.sub(0), Constant((0., 0.)), top_bottom)
bc1 = DirichletBC(W.sub(1), dp , left)
bc2 = DirichletBC(W.sub(1), Constant(0), right)
bc3 = DirichletBC(W.sub(0).sub(1), Constant(0.), left)
bc4 = DirichletBC(W.sub(0).sub(1), Constant(0.), right)
bcs = [bc0,bc1,bc2,bc3,bc4]
bndterm = dp*dot(v,Constant((-1.,0.)))*ds(1)
a = eta*inner(grad(u), grad(v))*dx - div(v)*p*dx + q*div(u)*dx+alpha*dot(u,v)*dx#+bndterm
L = inner(Constant((0.,0.)), v)*dx -bndterm
U = Function(W)
solve(a == L, U, bcs)
u, ps = U.split()
#SOLVE CONCENTRATION
mm = mesh_metric2(mesh)
vdir = u/sqrt(inner(u,u)+DOLFIN_EPS)
if iii == 0 or use_reform == False:
Q2 = FunctionSpace(mesh,'CG',2); c = Function(Q2)
q = TestFunction(Q2); p = TrialFunction(Q2)
newq = (q+dot(vdir,dot(mm,vdir))*inner(grad(q),vdir)) #SUPG
if use_reform:
F = newq*(fac/((1+exp(-c))**2)*exp(-c))*inner(grad(c),u)*dx
J = derivative(F,c)
bc = DirichletBC(Q2, Expression("-log("+str(float(fac)) +"/("+testsol+"+"+str(float(delta))+")-1)"), left)
# bc = DirichletBC(Q, -ln(fac/(Expression(testsol)+delta)-1), left)
problem = NonlinearVariationalProblem(F,c,bc,J)
solver = NonlinearVariationalSolver(problem)
solver.parameters["newton_solver"]["relaxation_parameter"] = relp
solver.solve()
else:
a2 = newq*inner(grad(p),u)*dx
bc = DirichletBC(Q2, Expression(testsol), left)
L2 = Constant(0.)*q*dx
solve(a2 == L2, c, bc)
if (not bool(use_adapt)) or iii == Nadapt-1:
break
um = project(sqrt(inner(u,u)),FunctionSpace(mesh,'CG',2))
H = metric_pnorm(um, eta, max_edge_ratio=1+49*(use_adapt!=2), p=2)
H2 = metric_pnorm(c, eta, max_edge_ratio=1+49*(use_adapt!=2), p=2)
#H3 = metric_pnorm(ps , eta, max_edge_ratio=1+49*(use_adapt!=2), p=2)
H4 = metric_ellipse(H,H2)
#H5 = metric_ellipse(H3,H4,mesh)
mesh = adapt(H4)
if use_reform:
Q2 = FunctionSpace(mesh,'CG',2)
c = interpolate(c,Q2)
if use_reform:
c = project(fac/(1+exp(-c))-delta,FunctionSpace(mesh,'CG',2))
L2error = bnderror(c,Expression(testsol),ds)
dofs.append(len(c.vector().array())+len(U.vector().array()))
L2errors.append(L2error)
# fid = open("DOFS_L2errors_mesh_c_CG"+str(CGorder)+outname+".mpy",'w')
# pickle.dump([dofs[0],L2errors[0],c.vector().array().min(),c.vector().array().max()-1,mesh.cells(),mesh.coordinates(),c.vector().array()],fid)
# fid.close();
log(INFO+1,"%1dX ADAPT<->SOLVE complete: DOF=%5d, error=%0.0e, min(c)=%0.0e,max(c)-1=%0.0e" % (Nadapt, dofs[len(dofs)-1], L2error,c.vector().array().min(),c.vector().array().max()-1))
# PLOT MESH + solution
figure()
testf = interpolate(c ,FunctionSpace(mesh,'CG',1))
testfe = interpolate(Expression(testsol),FunctionSpace(mesh,'CG',1))
vtx2dof = vertex_to_dof_map(FunctionSpace(mesh, "CG" ,1))
zz = testf.vector().array()[vtx2dof]; zz[zz==1] -= 1e-16
hh=tricontourf(mesh.coordinates()[:,0],mesh.coordinates()[:,1],mesh.cells(),zz,100,cmap=get_cmap('binary'))
colorbar(hh)
hold('on'); triplot(mesh.coordinates()[:,0],mesh.coordinates()[:,1],mesh.cells(),color='r',linewidth=0.5); hold('off')
axis('equal'); box('off')
# savefig(outname+'final_mesh_CG2.png',dpi=300) #; savefig('outname+final_mesh_CG2.eps',dpi=300)
#PLOT ERROR
figure()
xe = interpolate(Expression("x[0]"),FunctionSpace(mesh,'CG',1)).vector().array()
ye = interpolate(Expression("x[1]"),FunctionSpace(mesh,'CG',1)).vector().array()
I = xe - Lx/2 > -DOLFIN_EPS; I2 = ye[I].argsort()
pyplot(ye[I][I2],testf.vector().array()[I][I2]-testfe.vector().array()[I][I2],'-b'); ylabel('error')
# PLOT L2error graph
figure()
pyloglog(dofs,L2errors,'-b.',linewidth=2,markersize=16); xlabel('Degree of freedoms'); ylabel('L2 error')
# SAVE SOLUTION
dofs = array(dofs); L2errors = array(L2errors)
fid = open("DOFS_L2errors_CG"+str(CGorder)+outname+".mpy",'w')
pickle.dump([dofs,L2errors],fid)
fid.close();
# #show()
# #LOAD SAVED SOLUTIONS
# fid = open("DOFS_L2errors_CG2"+outname+".mpy",'r')
# [dofs,L2errors] = pickle.load(fid)
# fid.close()
#
# PERFORM FITS ON LAST THREE POINTS
NfitP = 5
I = array(range(len(dofs)-NfitP,len(dofs)))
slope,ints = polyfit(pylog(dofs[I]), pylog(L2errors[I]), 1)
fid = open("DOFS_L2errors_CG2_fit"+outname+".mpy",'w')
pickle.dump([dofs,L2errors,slope,ints],fid)
fid.close()
#PLOT THEM TOGETHER
if CGorderL != [2]:
fid = open("DOFS_L2errors_CG3.mpy",'r')
[dofs_old,L2errors_old] = pickle.load(fid)
fid.close()
slope2,ints2 = polyfit(pylog(dofs_old[I]), pylog(L2errors_old[I]), 1)
figure()
pyloglog(dofs,L2errors,'-b.',dofs_old,L2errors_old,'--b.',linewidth=2,markersize=16)
hold('on'); pyloglog(dofs,pyexp2(ints)*dofs**slope,'-r',dofs_old,pyexp2(ints2)*dofs_old**slope2,'--r',linewidth=1); hold('off')
xlabel('Degree of freedoms'); ylabel('L2 error')
legend(['CG2','CG3',"%0.2f*log(DOFs)" % slope, "%0.2f*log(DOFs)" % slope2]) #legend(['new data','old_data'])
# savefig('comparison.png',dpi=300) #savefig('comparison.eps');
if not noplot:
show()