def burgers_spacedisc(N=10, nu=None, x0=0.0, xE=1.0, retfemdict=False,
condensemats=True):
mesh = dolfin.IntervalMesh(N, x0, xE)
V = dolfin.FunctionSpace(mesh, 'CG', 1)
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
# boundaries and conditions
ugamma = dolfin.Expression('0', degree=1)
def _spaceboundary(x, on_boundary):
return on_boundary
diribc = dolfin.DirichletBC(V, ugamma, _spaceboundary)
mass = assemble(v*u*dx)
stif = assemble(nu*inner(nabla_grad(v), nabla_grad(u))*dx)
M = dts.mat_dolfin2sparse(mass)
A = dts.mat_dolfin2sparse(stif)
M, _, bcdict = dts.condense_velmatsbybcs(M, [diribc], return_bcinfo=True)
ininds = bcdict['ininds']
A, rhsa = dts.condense_velmatsbybcs(A, [diribc])
def burger_nonl(vvec, t):
v0 = expandvfunc(vvec, V=V, ininds=ininds)
bnl = assemble(0.5*v*((v0*v0).dx(0))*dx)
return bnl.array()[ininds]
if retfemdict:
return M, A, rhsa, burger_nonl, dict(V=V, diribc=diribc, ininds=ininds)
else:
return M, A, rhsa, burger_nonl
def get_burgertensor_spacecomp(V=None, podmat=None, ininds=None, diribc=None,
Ukyleft=None, bwd=False,
**kwargs):
if not podmat.shape[0] == len(ininds):
raise Warning("Looks like this is not the right POD basis")
if Ukyleft is None:
Ukyleft = podmat
v = dolfin.TestFunction(V)
u = dolfin.TrialFunction(V)
if bwd:
uvvdxl = []
for ui in podmat.T:
hatui = expandvfunc(ui, V=V, ininds=ininds)
uivvdx = assemble(hatui*v*((u).dx(0))*dx)
Uivvdx = dts.mat_dolfin2sparse(uivvdx)
Uivvdx, _ = dts.condense_velmatsbybcs(Uivvdx, [diribc])
uvvdxl.append(np.dot(Ukyleft.T, Uivvdx*podmat))
else:
uvvdxl = []
for ui in podmat.T:
hatui = expandvfunc(ui, V=V, ininds=ininds)
uivvdx = assemble(0.5*hatui*((v*u).dx(0))*dx)
Uivvdx = dts.mat_dolfin2sparse(uivvdx)
Uivvdx, _ = dts.condense_velmatsbybcs(Uivvdx, [diribc])
uvvdxl.append(np.dot(Ukyleft.T, Uivvdx*podmat))
return uvvdxl
def get_pavrg_onsubd(odcoo=None, Q=None, ppin=None):
"""assemble matrix that returns the pressure average over a subdomain
"""
odom = ContDomain(odcoo)
q = dolfin.TrialFunction(Q)
p = dolfin.TestFunction(Q)
# factor to compute the average via \bar u = 1/h \int_0^h u(x) dx
Ci = 1.0 / ((odcoo['xmax'] - odcoo['xmin']) *
(odcoo['ymax'] - odcoo['ymin']))
charfun = CharactFun(odom)
# TODO: no need to have `p` and then sum up all rows
# TODO: integrate over subdomain rather than using `charfun`
cp = dolfin.assemble(Ci * p * q * charfun * dx)
CP = dts.mat_dolfin2sparse(cp)
ccp = sps.csc_matrix(CP.sum(axis=0))
if ppin is None:
return ccp # np.atleast_2d(cp.array())
else:
raise UserWarning('Need to implement/specify the pinned pressure')
def check_ass_penaro(bcsd=None, bcssfuns=None, V=None, plot=False):
mesh = V.mesh()
bcone = bcsd[1]
contshfunone = bcssfuns[1]
Gammaone = bcone()
bparts = dolfin.MeshFunction('size_t', mesh, mesh.topology().dim() - 1)
Gammaone.mark(bparts, 0)
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
# Robin boundary form
arob = dolfin.inner(u, v) * dolfin.ds(0)
brob = dolfin.inner(v, contshfunone) * dolfin.ds(0)
amatrob = dolfin.assemble(arob, exterior_facet_domains=bparts)
bmatrob = dolfin.assemble(brob, exterior_facet_domains=bparts)
amatrob = dts.mat_dolfin2sparse(amatrob)
amatrob.eliminate_zeros()
print 'Number of nonzeros in amatrob:', amatrob.nnz
bmatrob = bmatrob.array() # [ININDS]
if plot:
plt.figure(2)
plt.spy(amatrob)
if plot:
plt.figure(1)
for x in contshfunone.xs:
plt.plot(x[0], x[1], 'bo')
plt.show()
def check_ass_penaro(bcsd=None, bcssfuns=None, V=None, plot=False):
mesh = V.mesh()
bcone = bcsd[1]
contshfunone = bcssfuns[1]
Gammaone = bcone()
bparts = dolfin.MeshFunction('size_t', mesh, mesh.topology().dim() - 1)
Gammaone.mark(bparts, 0)
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
# Robin boundary form
arob = dolfin.inner(u, v) * dolfin.ds(0)
brob = dolfin.inner(v, contshfunone) * dolfin.ds(0)
amatrob = dolfin.assemble(arob, exterior_facet_domains=bparts)
bmatrob = dolfin.assemble(brob, exterior_facet_domains=bparts)
amatrob = dts.mat_dolfin2sparse(amatrob)
amatrob.eliminate_zeros()
print('Number of nonzeros in amatrob:', amatrob.nnz)
bmatrob = bmatrob.array() # [ININDS]
if plot:
plt.figure(2)
plt.spy(amatrob)
if plot:
plt.figure(1)
for x in contshfunone.xs:
plt.plot(x[0], x[1], 'bo')
plt.show()
def test_conv_asquad(self):
import dolfin_navier_scipy as dns
from dolfin import dx, grad, inner
import dolfin_navier_scipy.dolfin_to_sparrays as dts
femp, stokesmatsc, rhsd = \
dns.problem_setups.get_sysmats(problem='drivencavity', nu=1e-2,
mergerhs=True, meshparams={'N': 15})
invinds = femp['invinds']
V = femp['V']
hmat = dns.dolfin_to_sparrays.\
ass_convmat_asmatquad(W=femp['V'], invindsw=invinds)
xexp = '(1-x[0])*x[0]*(1-x[1])*x[1]*x[0]+2'
yexp = '(1-x[0])*x[0]*(1-x[1])*x[1]*x[1]+1'
# yexp = 'x[0]*x[0]*x[1]*x[1]'
f = dolfin.Expression((xexp, yexp), element=self.V.ufl_element())
u = dolfin.interpolate(f, V)
uvec = np.atleast_2d(u.vector().get_local()).T
uvec_gamma = uvec.copy()
uvec_gamma[invinds] = 0
u_gamma = dolfin.Function(V)
u_gamma.vector().set_local(uvec_gamma)
uvec_i = 0 * uvec
uvec_i[invinds, :] = uvec[invinds]
u_i = dolfin.Function(V)
u_i.vector().set_local(uvec_i)
# Assemble the 'actual' form
w = dolfin.TrialFunction(V)
wt = dolfin.TestFunction(V)
nform = dolfin.assemble(inner(grad(w) * u, wt) * dx)
# rows, cols, values = nform.data()
nmat = dts.mat_dolfin2sparse(nform)
# consider only the 'inner' equations
nmatrc = nmat[invinds, :][:, :]
# the boundary terms
N1, N2, fv = dns.dolfin_to_sparrays.\
get_convmats(u0_dolfun=u_gamma, V=V)
# print np.linalg.norm(nmatrc * uvec_i + nmatrc * uvec_gamma)
classicalconv = nmatrc * uvec
quadconv = (hmat * np.kron(uvec[invinds], uvec[invinds])
+ ((N1 + N2) * uvec_i)[invinds, :] + fv[invinds, :])
self.assertTrue(np.allclose(classicalconv, quadconv))
# print 'consistency tests'
self.assertTrue((np.linalg.norm(uvec[invinds])
- np.linalg.norm(uvec_i)) < 1e-14)
self.assertTrue(np.linalg.norm(uvec - uvec_gamma - uvec_i) < 1e-14)
def test_conv_asquad(self):
import dolfin_navier_scipy as dns
from dolfin import dx, grad, inner
import dolfin_navier_scipy.dolfin_to_sparrays as dts
femp, stokesmatsc, rhsd = \
dns.problem_setups.get_sysmats(problem='drivencavity', nu=1e-2,
mergerhs=True, meshparams={'N': 15})
invinds = femp['invinds']
V = femp['V']
hmat = dns.dolfin_to_sparrays.\
ass_convmat_asmatquad(W=femp['V'], invindsw=invinds)
xexp = '(1-x[0])*x[0]*(1-x[1])*x[1]*x[0]+2'
yexp = '(1-x[0])*x[0]*(1-x[1])*x[1]*x[1]+1'
# yexp = 'x[0]*x[0]*x[1]*x[1]'
f = dolfin.Expression((xexp, yexp), element=self.V.ufl_element())
u = dolfin.interpolate(f, V)
uvec = np.atleast_2d(u.vector().get_local()).T
uvec_gamma = uvec.copy()
uvec_gamma[invinds] = 0
u_gamma = dolfin.Function(V)
u_gamma.vector().set_local(uvec_gamma)
uvec_i = 0 * uvec
uvec_i[invinds, :] = uvec[invinds]
u_i = dolfin.Function(V)
u_i.vector().set_local(uvec_i)
# Assemble the 'actual' form
w = dolfin.TrialFunction(V)
wt = dolfin.TestFunction(V)
nform = dolfin.assemble(inner(grad(w) * u, wt) * dx)
# rows, cols, values = nform.data()
nmat = dts.mat_dolfin2sparse(nform)
# consider only the 'inner' equations
nmatrc = nmat[invinds, :][:, :]
# the boundary terms
N1, N2, fv = dns.dolfin_to_sparrays.\
get_convmats(u0_dolfun=u_gamma, V=V)
# print np.linalg.norm(nmatrc * uvec_i + nmatrc * uvec_gamma)
classicalconv = nmatrc * uvec
quadconv = (hmat * np.kron(uvec[invinds], uvec[invinds]) +
((N1 + N2) * uvec_i)[invinds, :] + fv[invinds, :])
self.assertTrue(np.allclose(classicalconv, quadconv))
# print 'consistency tests'
self.assertTrue(
(np.linalg.norm(uvec[invinds]) - np.linalg.norm(uvec_i)) < 1e-14)
self.assertTrue(np.linalg.norm(uvec - uvec_gamma - uvec_i) < 1e-14)
import dolfin import dolfin_navier_scipy.dolfin_to_sparrays as dts N = 20 mesh = dolfin.UnitSquareMesh(N, N) V = dolfin.FunctionSpace(mesh, 'CG', 1) u = dolfin.TrialFunction(V) v = dolfin.TestFunction(V) mass = dolfin.assemble(v*u*dolfin.dx) M = dts.mat_dolfin2sparse(mass)
import dolfin
import dolfin_navier_scipy.dolfin_to_sparrays as dts
from scipy.io import mmwrite
N = 25
mesh = dolfin.UnitSquareMesh(N, N)
V = dolfin.FunctionSpace(mesh, 'CG', 1)
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
mass = dolfin.assemble(v*u*dolfin.dx)
massmat = dts.mat_dolfin2sparse(mass)
matstring = 'testdata/massmat_square_CG1_N{0}'.format(N)
mmwrite(matstring, massmat)
def vdxop(vvec):
v0 = expandvfunc(vvec, V=V, ininds=ininds)
bnl = assemble((v*v0*u.dx(0))*dx)
Bnl = dts.mat_dolfin2sparse(bnl)
Bnl, rhsa = dts.condense_velmatsbybcs(Bnl, [diribc])
return Bnl
