def get_bc_parts(mesh, lst):
"""
Build a size_t function with boundary condition parts.
Returns all Robin and Steklov conditions that need to be applied,
the shift needed to get a nonnegative function,
and the function itself.
"""
if len(lst) > 0:
shift = max(0, -min(e.value for e in lst))
else:
return [], [], 0, FacetFunction("size_t", mesh, 0)
# values must be shifted by smallest Steklov value since size_t is unsigned
fun = FacetFunction("size_t", mesh, shift)
for bc in lst:
sub = OnBoundary()
# overwrite inside function with the one from bc
sub.inside = bc.getTest()
sub.mark(fun, bc.value + shift)
# some conditions may cancel eachother
exist = set(np.unique(fun.array()))
lst = [e for e in lst if e.value+shift in exist]
# separate Robin and Steklov, Dirichlet and Neumann are irrelevant
Robin = [e for e in lst if e.value > 1 and e.parValue != 0]
Steklov = [e for e in lst if e.value < 0 and e.parValue != 0]
return Robin, Steklov, shift, fun
def get_bc_parts(mesh, lst):
"""
Build a size_t function with boundary condition parts.
Returns all Robin and Steklov conditions that need to be applied,
the shift needed to get a nonnegative function,
and the function itself.
"""
if len(lst) > 0:
shift = max(0, -min(e.value for e in lst))
else:
return [], [], 0, FacetFunction("size_t", mesh, 0)
# values must be shifted by smallest Steklov value since size_t is unsigned
fun = FacetFunction("size_t", mesh, shift)
for bc in lst:
sub = OnBoundary()
# overwrite inside function with the one from bc
sub.inside = bc.getTest()
sub.mark(fun, bc.value + shift)
# some conditions may cancel eachother
exist = set(np.unique(fun.array()))
lst = [e for e in lst if e.value + shift in exist]
# separate Robin and Steklov, Dirichlet and Neumann are irrelevant
Robin = [e for e in lst if e.value > 1 and e.parValue != 0]
Steklov = [e for e in lst if e.value < 0 and e.parValue != 0]
return Robin, Steklov, shift, fun
def mark_conditions(mesh, lst):
""" Mark all boundary conditions from the list. """
fun = FacetFunction("int", mesh, 0)
for bc in lst:
sub = OnBoundary()
# overwrite inside function with the one from bc
sub.inside = bc.getTest()
sub.mark(fun, bc.value)
return fun.array()
def mark_conditions(mesh, lst):
""" Mark all boundary conditions from the list. """
fun = FacetFunction("int", mesh, 0)
for bc in lst:
sub = OnBoundary()
# overwrite inside function with the one from bc
sub.inside = bc.getTest()
sub.mark(fun, bc.value)
return fun.array()
def derived_bcs(V, original_bcs, u_):
new_bcs = []
# Check first if user has declared subdomains
subdomain = original_bcs[0].user_sub_domain()
if subdomain is None:
mesh = V.mesh()
ff = FacetFunction("size_t", mesh, 0)
for i, bc in enumerate(original_bcs):
bc.apply(u_[0].vector()) # Need to initialize bc
m = bc.markers() # Get facet indices of boundary
ff.array()[m] = i + 1
new_bcs.append(DirichletBC(V, Constant(0), ff, i + 1))
else:
for i, bc in enumerate(original_bcs):
subdomain = bc.user_sub_domain()
new_bcs.append(DirichletBC(V, Constant(0), subdomain))
return new_bcs
def derived_bcs(V, original_bcs, u_):
new_bcs = []
# Check first if user has declared subdomains
subdomain = original_bcs[0].user_sub_domain()
if subdomain is None:
mesh = V.mesh()
ff = FacetFunction("size_t", mesh, 0)
for i, bc in enumerate(original_bcs):
bc.apply(u_[0].vector()) # Need to initialize bc
m = bc.markers() # Get facet indices of boundary
ff.array()[m] = i + 1
new_bcs.append(DirichletBC(V, Constant(0), ff, i + 1))
else:
for i, bc in enumerate(original_bcs):
subdomain = bc.user_sub_domain()
new_bcs.append(DirichletBC(V, Constant(0), subdomain))
return new_bcs
def les_setup(u_, mesh, assemble_matrix, CG1Function, nut_krylov_solver, bcs,
**NS_namespace):
"""
Set up for solving the Germano Dynamic LES model applying
Lagrangian Averaging.
"""
# Create function spaces
CG1 = FunctionSpace(mesh, "CG", 1)
p, q = TrialFunction(CG1), TestFunction(CG1)
dim = mesh.geometry().dim()
# Define delta and project delta**2 to CG1
delta = pow(CellVolume(mesh), 1. / dim)
delta_CG1_sq = project(delta, CG1)
delta_CG1_sq.vector().set_local(delta_CG1_sq.vector().array()**2)
delta_CG1_sq.vector().apply("insert")
# Define nut_
Sij = sym(grad(u_))
magS = sqrt(2 * inner(Sij, Sij))
Cs = Function(CG1)
nut_form = Cs**2 * delta**2 * magS
# Create nut_ BCs
ff = FacetFunction("size_t", mesh, 0)
bcs_nut = []
for i, bc in enumerate(bcs['u0']):
bc.apply(u_[0].vector()) # Need to initialize bc
m = bc.markers() # Get facet indices of boundary
ff.array()[m] = i + 1
bcs_nut.append(DirichletBC(CG1, Constant(0), ff, i + 1))
nut_ = CG1Function(nut_form,
mesh,
method=nut_krylov_solver,
bcs=bcs_nut,
bounded=True,
name="nut")
# Create functions for holding the different velocities
u_CG1 = as_vector([Function(CG1) for i in range(dim)])
u_filtered = as_vector([Function(CG1) for i in range(dim)])
dummy = Function(CG1)
ll = LagrangeInterpolator()
# Assemble required filter matrices and functions
G_under = Function(CG1, assemble(TestFunction(CG1) * dx))
G_under.vector().set_local(1. / G_under.vector().array())
G_under.vector().apply("insert")
G_matr = assemble(inner(p, q) * dx)
# Set up functions for Lij and Mij
Lij = [Function(CG1) for i in range(dim * dim)]
Mij = [Function(CG1) for i in range(dim * dim)]
# Check if case is 2D or 3D and set up uiuj product pairs and
# Sij forms, assemble required matrices
Sijcomps = [Function(CG1) for i in range(dim * dim)]
Sijfcomps = [Function(CG1) for i in range(dim * dim)]
# Assemble some required matrices for solving for rate of strain terms
Sijmats = [assemble_matrix(p.dx(i) * q * dx) for i in range(dim)]
if dim == 3:
tensdim = 6
uiuj_pairs = ((0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2))
else:
tensdim = 3
uiuj_pairs = ((0, 0), (0, 1), (1, 1))
# Set up Lagrange functions
JLM = Function(CG1)
JLM.vector()[:] += 1E-32
JMM = Function(CG1)
JMM.vector()[:] += 1
return dict(Sij=Sij,
nut_form=nut_form,
nut_=nut_,
delta=delta,
bcs_nut=bcs_nut,
delta_CG1_sq=delta_CG1_sq,
CG1=CG1,
Cs=Cs,
u_CG1=u_CG1,
u_filtered=u_filtered,
ll=ll,
Lij=Lij,
Mij=Mij,
Sijcomps=Sijcomps,
Sijfcomps=Sijfcomps,
Sijmats=Sijmats,
JLM=JLM,
JMM=JMM,
dim=dim,
tensdim=tensdim,
G_matr=G_matr,
G_under=G_under,
dummy=dummy,
uiuj_pairs=uiuj_pairs)
def marked_boundary(mesh):
""" Return array of vertex values with 1 on boundary, 0 otherwise. """
fun = FacetFunction("int", mesh, 0)
on = OnBoundary()
on.mark(fun, 1)
return fun.array()
def solve(self):
""" Find eigenvalues for transformed mesh. """
self.progress("Building mesh.")
# build transformed mesh
mesh = self.refineMesh()
# dim = mesh.topology().dim()
if self.bcLast:
mesh = transform_mesh(mesh, self.transformList)
Robin, Steklov, shift, bcs = get_bc_parts(mesh, self.bcList)
else:
Robin, Steklov, shift, bcs = get_bc_parts(mesh, self.bcList)
mesh = transform_mesh(mesh, self.transformList)
# boundary conditions computed on non-transformed mesh
# copy the values to transformed mesh
fun = FacetFunction("size_t", mesh, shift)
fun.array()[:] = bcs.array()[:]
bcs = fun
ds = Measure('ds', domain=mesh, subdomain_data=bcs)
V = FunctionSpace(mesh, self.method, self.deg)
u = TrialFunction(V)
v = TestFunction(V)
self.progress("Assembling matrices.")
wTop = Expression(self.wTop, degree=self.deg)
wBottom = Expression(self.wBottom, degree=self.deg)
#
# build stiffness matrix form
#
s = dot(grad(u), grad(v))*wTop*dx
# add Robin parts
for bc in Robin:
s += Constant(bc.parValue)*u*v*wTop*ds(bc.value+shift)
#
# build mass matrix form
#
if len(Steklov) > 0:
m = 0
for bc in Steklov:
m += Constant(bc.parValue)*u*v*wBottom*ds(bc.value+shift)
else:
m = u*v*wBottom*dx
# assemble
# if USE_EIGEN:
# S, M = EigenMatrix(), EigenMatrix()
# tempv = EigenVector()
# else:
S, M = PETScMatrix(), PETScMatrix()
# tempv = PETScVector()
if not np.any(bcs.array() == shift+1):
# no Dirichlet parts
assemble(s, tensor=S)
assemble(m, tensor=M)
else:
#
# with EIGEN we could
# apply Dirichlet condition symmetrically
# completely remove rows and columns
#
# Dirichlet parts are marked with shift+1
#
# temp = Constant(0)*v*dx
bc = DirichletBC(V, Constant(0.0), bcs, shift+1)
# assemble_system(s, temp, bc, A_tensor=S, b_tensor=tempv)
# assemble_system(m, temp, bc, A_tensor=M, b_tensor=tempv)
assemble(s, tensor=S)
bc.apply(S)
assemble(m, tensor=M)
# bc.zero(M)
# if USE_EIGEN:
# M = M.sparray()
# M.eliminate_zeros()
# print M.shape
# indices = M.indptr[:-1] - M.indptr[1:] < 0
# M = M[indices, :].tocsc()[:, indices]
# S = S.sparray()[indices, :].tocsc()[:, indices]
# print M.shape
#
# solve the eigenvalue problem
#
self.progress("Solving eigenvalue problem.")
eigensolver = SLEPcEigenSolver(S, M)
eigensolver.parameters["problem_type"] = "gen_hermitian"
eigensolver.parameters["solver"] = "krylov-schur"
if self.target is not None:
eigensolver.parameters["spectrum"] = "target real"
eigensolver.parameters["spectral_shift"] = self.target
else:
eigensolver.parameters["spectrum"] = "smallest magnitude"
eigensolver.parameters["spectral_shift"] = -0.01
eigensolver.parameters["spectral_transform"] = "shift-and-invert"
eigensolver.solve(self.number)
self.progress("Generating eigenfunctions.")
if eigensolver.get_number_converged() == 0:
return None
eigf = []
eigv = []
if self.deg > 1:
mesh = refine(mesh)
W = FunctionSpace(mesh, 'CG', 1)
for i in range(eigensolver.get_number_converged()):
pair = eigensolver.get_eigenpair(i)[::2]
eigv.append(pair[0])
u = Function(V)
u.vector()[:] = pair[1]
eigf.append(interpolate(u, W))
return eigv, eigf
def les_setup(u_, mesh, assemble_matrix, CG1Function, nut_krylov_solver, bcs, **NS_namespace):
"""
Set up for solving the Germano Dynamic LES model applying
Lagrangian Averaging.
"""
# Create function spaces
CG1 = FunctionSpace(mesh, "CG", 1)
p, q = TrialFunction(CG1), TestFunction(CG1)
dim = mesh.geometry().dim()
# Define delta and project delta**2 to CG1
delta = pow(CellVolume(mesh), 1./dim)
delta_CG1_sq = project(delta, CG1)
delta_CG1_sq.vector().set_local(delta_CG1_sq.vector().array()**2)
delta_CG1_sq.vector().apply("insert")
# Define nut_
Sij = sym(grad(u_))
magS = sqrt(2*inner(Sij,Sij))
Cs = Function(CG1)
nut_form = Cs**2 * delta**2 * magS
# Create nut_ BCs
ff = FacetFunction("size_t", mesh, 0)
bcs_nut = []
for i, bc in enumerate(bcs['u0']):
bc.apply(u_[0].vector()) # Need to initialize bc
m = bc.markers() # Get facet indices of boundary
ff.array()[m] = i+1
bcs_nut.append(DirichletBC(CG1, Constant(0), ff, i+1))
nut_ = CG1Function(nut_form, mesh, method=nut_krylov_solver, bcs=bcs_nut, bounded=True, name="nut")
# Create functions for holding the different velocities
u_CG1 = as_vector([Function(CG1) for i in range(dim)])
u_filtered = as_vector([Function(CG1) for i in range(dim)])
dummy = Function(CG1)
ll = LagrangeInterpolator()
# Assemble required filter matrices and functions
G_under = Function(CG1, assemble(TestFunction(CG1)*dx))
G_under.vector().set_local(1./G_under.vector().array())
G_under.vector().apply("insert")
G_matr = assemble(inner(p,q)*dx)
# Set up functions for Lij and Mij
Lij = [Function(CG1) for i in range(dim*dim)]
Mij = [Function(CG1) for i in range(dim*dim)]
# Check if case is 2D or 3D and set up uiuj product pairs and
# Sij forms, assemble required matrices
Sijcomps = [Function(CG1) for i in range(dim*dim)]
Sijfcomps = [Function(CG1) for i in range(dim*dim)]
# Assemble some required matrices for solving for rate of strain terms
Sijmats = [assemble_matrix(p.dx(i)*q*dx) for i in range(dim)]
if dim == 3:
tensdim = 6
uiuj_pairs = ((0,0),(0,1),(0,2),(1,1),(1,2),(2,2))
else:
tensdim = 3
uiuj_pairs = ((0,0),(0,1),(1,1))
# Set up Lagrange functions
JLM = Function(CG1)
JLM.vector()[:] += 1E-32
JMM = Function(CG1)
JMM.vector()[:] += 1
return dict(Sij=Sij, nut_form=nut_form, nut_=nut_, delta=delta, bcs_nut=bcs_nut,
delta_CG1_sq=delta_CG1_sq, CG1=CG1, Cs=Cs, u_CG1=u_CG1,
u_filtered=u_filtered, ll=ll, Lij=Lij, Mij=Mij, Sijcomps=Sijcomps,
Sijfcomps=Sijfcomps, Sijmats=Sijmats, JLM=JLM, JMM=JMM, dim=dim,
tensdim=tensdim, G_matr=G_matr, G_under=G_under, dummy=dummy,
uiuj_pairs=uiuj_pairs)
def marked_boundary(mesh):
""" Return array of vertex values with 1 on boundary, 0 otherwise. """
fun = FacetFunction("int", mesh, 0)
on = OnBoundary()
on.mark(fun, 1)
return fun.array()
def solve(self):
""" Find eigenvalues for transformed mesh. """
self.progress("Building mesh.")
# build transformed mesh
mesh = self.refineMesh()
# dim = mesh.topology().dim()
if self.bcLast:
mesh = transform_mesh(mesh, self.transformList)
Robin, Steklov, shift, bcs = get_bc_parts(mesh, self.bcList)
else:
Robin, Steklov, shift, bcs = get_bc_parts(mesh, self.bcList)
mesh = transform_mesh(mesh, self.transformList)
# boundary conditions computed on non-transformed mesh
# copy the values to transformed mesh
fun = FacetFunction("size_t", mesh, shift)
fun.array()[:] = bcs.array()[:]
bcs = fun
ds = Measure('ds', domain=mesh, subdomain_data=bcs)
V = FunctionSpace(mesh, self.method, self.deg)
u = TrialFunction(V)
v = TestFunction(V)
self.progress("Assembling matrices.")
wTop = Expression(self.wTop)
wBottom = Expression(self.wBottom)
#
# build stiffness matrix form
#
s = dot(grad(u), grad(v)) * wTop * dx
# add Robin parts
for bc in Robin:
s += Constant(bc.parValue) * u * v * wTop * ds(bc.value + shift)
#
# build mass matrix form
#
if len(Steklov) > 0:
m = 0
for bc in Steklov:
m += Constant(
bc.parValue) * u * v * wBottom * ds(bc.value + shift)
else:
m = u * v * wBottom * dx
# assemble
# if USE_EIGEN:
# S, M = EigenMatrix(), EigenMatrix()
# tempv = EigenVector()
# else:
S, M = PETScMatrix(), PETScMatrix()
# tempv = PETScVector()
if not np.any(bcs.array() == shift + 1):
# no Dirichlet parts
assemble(s, tensor=S)
assemble(m, tensor=M)
else:
#
# with EIGEN we could
# apply Dirichlet condition symmetrically
# completely remove rows and columns
#
# Dirichlet parts are marked with shift+1
#
# temp = Constant(0)*v*dx
bc = DirichletBC(V, Constant(0.0), bcs, shift + 1)
# assemble_system(s, temp, bc, A_tensor=S, b_tensor=tempv)
# assemble_system(m, temp, bc, A_tensor=M, b_tensor=tempv)
assemble(s, tensor=S)
bc.apply(S)
assemble(m, tensor=M)
# bc.zero(M)
# if USE_EIGEN:
# M = M.sparray()
# M.eliminate_zeros()
# print M.shape
# indices = M.indptr[:-1] - M.indptr[1:] < 0
# M = M[indices, :].tocsc()[:, indices]
# S = S.sparray()[indices, :].tocsc()[:, indices]
# print M.shape
#
# solve the eigenvalue problem
#
self.progress("Solving eigenvalue problem.")
eigensolver = SLEPcEigenSolver(S, M)
eigensolver.parameters["problem_type"] = "gen_hermitian"
eigensolver.parameters["solver"] = "krylov-schur"
if self.target is not None:
eigensolver.parameters["spectrum"] = "target real"
eigensolver.parameters["spectral_shift"] = self.target
else:
eigensolver.parameters["spectrum"] = "smallest magnitude"
eigensolver.parameters["spectral_shift"] = -0.01
eigensolver.parameters["spectral_transform"] = "shift-and-invert"
eigensolver.solve(self.number)
self.progress("Generating eigenfunctions.")
if eigensolver.get_number_converged() == 0:
return None
eigf = []
eigv = []
if self.deg > 1:
mesh = refine(mesh)
W = FunctionSpace(mesh, 'CG', 1)
for i in range(eigensolver.get_number_converged()):
pair = eigensolver.get_eigenpair(i)[::2]
eigv.append(pair[0])
u = Function(V)
u.vector()[:] = pair[1]
eigf.append(interpolate(u, W))
return eigv, eigf
