def test_comparison_checker(self):
cell = triangle
element = FiniteElement("Lagrange", cell, 1)
u = TrialFunction(element)
v = TestFunction(element)
a = conditional(ge(abs(u), imag(v)), u, v)
b = conditional(le(sqrt(abs(u)), imag(v)), as_ufl(1), as_ufl(1j))
c = conditional(gt(abs(u), pow(imag(v), 0.5)), sin(u), cos(v))
d = conditional(lt(as_ufl(-1), as_ufl(1)), u, v)
e = max_value(as_ufl(0), real(u))
f = min_value(sin(u), cos(v))
g = min_value(sin(pow(u, 3)), cos(abs(v)))
assert do_comparison_check(a) == conditional(ge(real(abs(u)), real(imag(v))), u, v)
with pytest.raises(ComplexComparisonError):
b = do_comparison_check(b)
with pytest.raises(ComplexComparisonError):
c = do_comparison_check(c)
assert do_comparison_check(d) == conditional(lt(real(as_ufl(-1)), real(as_ufl(1))), u, v)
assert do_comparison_check(e) == max_value(real(as_ufl(0)), real(real(u)))
assert do_comparison_check(f) == min_value(real(sin(u)), real(cos(v)))
assert do_comparison_check(g) == min_value(real(sin(pow(u, 3))), real(cos(abs(v))))
def setup_problem(self, debug=False):
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
drho_integral = vectotal([
tdrho * wrho * self.dx
for tdrho, wrho in zip(self.tdrhos, self.wrhos)
])
dU_integral = vectotal(
[tdU * wU * self.dx for tdU, wU in zip(self.tdUs, self.wUs)])
self.A = fe.assemble(drho_integral + dU_integral)
for bc in self.bcs:
bc.apply(self.A)
self.dsol = Function(self.VS)
self.drhos = self.dsol.split()[:2**self.dim]
self.dUs = self.dsol.split()[2**self.dim:]
#
# These are the values of rho and U themselves (not their
# symmetrized versions) on all subdomains of the original
# domain.
#
if not hasattr(self, 'rhosds'):
self.rhosds = matmul(self.eomat, self.irhos)
# self.Usds is a list of nligands lists. Sublist i is of
# length 2**dim and lists the value of ligand i on each of the
# 2**dim subdomains.
#
if not hasattr(self, 'Usds'):
self.Usds = [
matmul(self.eomat,
self.iUs[i * 2**self.dim:(i + 1) * 2**self.dim])
for i in range(self.nligands)
]
#
# assemble RHS (for each time point, but compile only once)
#
if not hasattr(self, 'rho_terms'):
self.sigma = self.params['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rho_min = self.params['rho_min']
self.rhopen = self.params['rhopen']
self.grhopen = self.params['grhopen']
#
# Compute fluxes on subdomains.
# Vsds is a list of length 2**dim, the value of V on each
# subdomain.
#
self.Vsds = []
for Usd, rhosd in zip(zip(*self.Usds), self.rhosds):
self.Vsds.append(self.V(Usd, rhosd))
#
# I may need to adjust the signs of the subdomain vs by
# the symmetries of the combinations
#
self.vsds = [
-ufl.grad(Vsd) - (self.s2 * ufl.grad(rhosd) /
ufl.max_value(rhosd, self.rho_min))
for Vsd, rhosd in zip(self.Vsds, self.rhosds)
]
self.fluxsds = [
vsd * rhosd for vsd, rhosd in zip(self.vsds, self.rhosds)
]
self.vnsds = [
ufl.max_value(ufl.dot(vsd, self.n), 0) for vsd in self.vsds
]
self.facet_fluxsds = [
(vnsd('+') * ufl.max_value(rhosd('+'), 0.0) -
vnsd('-') * ufl.max_value(rhosd('-'), 0.0))
for vnsd, rhosd in zip(self.vnsds, self.rhosds)
]
#
# Now combine the subdomain fluxes to get the fluxes for
# the symmetrized functions
#
self.fluxs = matmul((2.0**-self.dim) * self.eomat, self.fluxsds)
self.facet_fluxs = matmul((2.0**-self.dim) * self.eomat,
self.facet_fluxsds)
self.rho_flux_jump = vectotal([
-facet_flux * ufl.jump(wrho) * self.dS
for facet_flux, wrho in zip(self.facet_fluxs, self.wrhos)
])
self.rho_grad_move = vectotal([
ufl.dot(flux, ufl.grad(wrho)) * self.dx
for flux, wrho in zip(self.fluxs, self.wrhos)
])
self.rho_penalty = vectotal([
-(self.rhopen * self.degree**2 / self.havg) *
ufl.dot(ufl.jump(rho, self.n), ufl.jump(wrho, self.n)) *
self.dS for rho, wrho in zip(self.irhos, self.wrhos)
])
self.grho_penalty = vectotal([
-self.grhopen * self.degree**2 *
(ufl.jump(ufl.grad(rho), self.n) *
ufl.jump(ufl.grad(wrho), self.n)) * self.dS
for rho, wrho in zip(self.irhos, self.wrhos)
])
self.rho_terms = (self.rho_flux_jump + self.rho_grad_move +
self.rho_penalty + self.grho_penalty)
if not hasattr(self, 'U_terms'):
self.U_min = self.params['U_min']
self.Upen = self.params['Upen']
self.gUpen = self.params['gUpen']
self.U_decay = 0.0
self.U_secretion = 0.0
self.jump_gUw = 0.0
self.U_diffusion = 0.0
self.U_penalty = 0.0
self.gU_penalty = 0.0
for j, lig in enumerate(self.ligands.ligands()):
sl = slice(j * 2**self.dim, (j + 1) * 2**self.dim)
self.U_decay += -lig.gamma * sum([
iUi * wUi * self.dx
for iUi, wUi in zip(self.iUs[sl], self.wUs[sl])
])
self.U_secretion += lig.s * sum([
rho * wU * self.dx
for rho, wU in zip(self.irhos, self.wUs[sl])
])
self.jump_gUw += lig.D * sum([
ufl.jump(wU * ufl.grad(U), self.n) * self.dS
for wU, U in zip(self.wUs[sl], self.iUs[sl])
])
self.U_diffusion += -lig.D * sum([
ufl.dot(ufl.grad(U), ufl.grad(wU)) * self.dx
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.U_penalty += -self.Upen * self.degree**2 * sum([
(1.0 / self.havg) * ufl.dot(ufl.jump(U, self.n),
ufl.jump(wU, self.n)) * self.dS
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.gU_penalty += -self.gUpen * self.degree**2 * sum([
ufl.jump(ufl.grad(U), self.n) *
ufl.jump(ufl.grad(wU), self.n) * self.dS
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty)
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
self.J_terms = fe.derivative(self.all_terms, self.sol)
def setup_problem(self, debug=False):
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
drho_integral = vectotal(
[tdrho*wrho*self.dx for tdrho,wrho in
zip(self.tdrhos, self.wrhos)]
)
dU_integral = vectotal(
[tdU*wU*self.dx
for tdU,wU in zip(self.tdUs, self.wUs)
]
)
self.A = fe.assemble(drho_integral + dU_integral)
for bc in self.bcs:
bc.apply(self.A)
# if self.solver_type == 'lu':
# self.solver = fe.LUSolver(
# self.A,
# )
# self.solver.parameters['reuse_factorization'] = True
# else:
# self.solver = fe.KrylovSolver(
# self.A,
# self.solver_type,
# self.preconditioner_type
# )
self.dsol = Function(self.VS)
self.drhos = self.dsol.split()[: 2**self.dim]
self.dUs = self.dsol.split()[2**self.dim :]
#
# These are the values of rho and U themselves (not their
# symmetrized versions) on all subdomains of the original
# domain.
#
if not hasattr(self, 'rhosds'):
self.rhosds = matmul(self.eomat, self.irhos)
if not hasattr(self, 'Usds'):
self.Usds = matmul(self.eomat, self.iUs)
#
# assemble RHS (for each time point, but compile only once)
#
if not hasattr(self, 'rho_terms'):
self.sigma = self.params['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rho_min = self.params['rho_min']
self.rhopen = self.params['rhopen']
self.grhopen = self.params['grhopen']
#
# Compute fluxes on subdomains.
#
self.Vsds = [self.V(Usd, rhosd) for Usd,rhosd in
zip(self.Usds, self.rhosds)]
#
# I may need to adjust the signs of the subdomain vs by
# the symmetries of the combinations
#
self.vsds = [-ufl.grad(Vsd) - (
self.s2*ufl.grad(rhosd)/ufl.max_value(rhosd, self.rho_min)
) for Vsd,rhosd in zip(self.Vsds, self.rhosds)]
self.fluxsds = [vsd * rhosd for vsd,rhosd in
zip(self.vsds, self.rhosds)]
self.vnsds = [ufl.max_value(ufl.dot(vsd, self.n), 0)
for vsd in self.vsds]
self.facet_fluxsds = [(
vnsd('+')*ufl.max_value(rhosd('+'), 0.0) -
vnsd('-')*ufl.max_value(rhosd('-'), 0.0)
) for vnsd,rhosd in zip(self.vnsds, self.rhosds)]
#
# Now combine the subdomain fluxes to get the fluxes for
# the symmetrized functions
#
self.fluxs = matmul((2.0**-self.dim)*self.eomat,
self.fluxsds)
self.facet_fluxs = matmul((2.0**-self.dim)*self.eomat,
self.facet_fluxsds)
self.rho_flux_jump = vectotal(
[-facet_flux*ufl.jump(wrho)*self.dS
for facet_flux,wrho in
zip(self.facet_fluxs, self.wrhos)]
)
self.rho_grad_move = vectotal(
[ufl.dot(flux, ufl.grad(wrho))*self.dx
for flux,wrho in
zip(self.fluxs, self.wrhos)]
)
self.rho_penalty = vectotal(
[-(self.rhopen * self.degree**2 / self.havg) *
ufl.dot(ufl.jump(rho, self.n),
ufl.jump(wrho, self.n)) * self.dS
for rho,wrho in zip(self.irhos, self.wrhos)]
)
self.grho_penalty = vectotal(
[-self.grhopen * self.degree**2 *
(ufl.jump(ufl.grad(rho), self.n) *
ufl.jump(ufl.grad(wrho), self.n)) * self.dS
for rho,wrho in zip(self.irhos, self.wrhos)]
)
self.rho_terms = (
self.rho_flux_jump + self.rho_grad_move +
self.rho_penalty + self.grho_penalty
)
if not hasattr(self, 'U_terms'):
self.U_min = self.params['U_min']
self.gamma = self.params['gamma']
self.s = self.params['s']
self.D = self.params['D']
self.Upen = self.params['Upen']
self.gUpen = self.params['gUpen']
self.U_decay = vectotal(
[-self.gamma * U * wU * self.dx
for U,wU in zip(self.iUs, self.wUs)]
)
self.U_secretion = vectotal(
[self.s * rho * wU * self.dx
for rho, wU in zip(self.irhos, self.wUs)]
)
self.jump_gUw = vectotal(
[self.D * ufl.jump(wU * ufl.grad(U), self.n) * self.dS
for wU, U in zip(self.wUs, self.iUs)
]
)
self.U_diffusion = vectotal(
[-self.D
* ufl.dot(ufl.grad(U), ufl.grad(wU))*self.dx
for U,wU in zip(self.iUs, self.wUs)
]
)
self.U_penalty = vectotal(
[-(self.Upen * self.degree**2 / self.havg)
* ufl.dot(ufl.jump(U, self.n), ufl.jump(wU, self.n))*self.dS
for U,wU in zip(self.iUs, self.wUs)
]
)
self.gU_penalty = vectotal(
[-self.gUpen * self.degree**2 *
ufl.jump(ufl.grad(U), self.n) *
ufl.jump(ufl.grad(wU), self.n) * self.dS
for U,wU in zip(self.iUs, self.wUs)
]
)
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty
)
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
self.J_terms = fe.derivative(self.all_terms, self.sol)
def setup_problem(self, t, debug=False):
self.set_time(t)
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
logVARIABLE('making matrix A')
self.drho_integral = sum([
tdrho * wrho * self.dx
for tdrho, wrho in zip(self.tdrhos, self.wrhos)
])
self.dU_integral = sum(
[tdU * wU * self.dx for tdU, wU in zip(self.tdUs, self.wUs)])
logVARIABLE('assembling A')
self.A = fe.PETScMatrix()
logVARIABLE('self.A', self.A)
fe.assemble(self.drho_integral + self.dU_integral, tensor=self.A)
logVARIABLE('A assembled. Applying BCs')
pA = fe.as_backend_type(self.A).mat()
Adiag = pA.getDiagonal()
logVARIABLE('Adiag.array', Adiag.array)
# self.A = fe.assemble(self.drho_integral + self.dU_integral +
# self.dP_integral)
for bc in self.bcs:
bc.apply(self.A)
Adiag = pA.getDiagonal()
logVARIABLE('Adiag.array', Adiag.array)
self.dsol = Function(self.VS)
dsolsplit = self.dsol.split()
self.drhos, self.dUs = (dsolsplit[:2**self.dim],
dsolsplit[2**self.dim:])
#
# assemble RHS (for each time point, but compile only once)
#
#
# These are the values of rho and U themselves (not their
# symmetrized versions) on all subdomains of the original
# domain.
#
if not hasattr(self, 'rhosds'):
self.rhosds = matmul(self.eomat, self.irhos)
# self.Usds is a list of nligands lists. Sublist i is of
# length 2**dim and lists the value of ligand i on each of the
# 2**dim subdomains.
#
if not hasattr(self, 'Usds'):
self.Usds = [
matmul(self.eomat,
self.iUs[i * 2**self.dim:(i + 1) * 2**self.dim])
for i in range(self.nligands)
]
if not hasattr(self, 'rho_terms'):
logVARIABLE('making rho_terms')
self.sigma = self.iparams['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rhomin = self.iparams['rhomin']
self.rhopen = self.iparams['rhopen']
self.grhopen = self.iparams['grhopen']
#
# Compute fluxes on subdomains.
# Vsds is a list of length 2**dim, the value of V on each
# subdomain.
#
self.Vsds = []
for Usd, rhosd in zip(zip(*self.Usds), self.rhosds):
self.Vsds.append(self.V(Usd, ufl.max_value(rhosd,
self.rhomin)))
self.vsds = [
-ufl.grad(Vsd) -
(self.s2 * ufl.grad(rhosd) / ufl.max_value(rhosd, self.rhomin))
for Vsd, rhosd in zip(self.Vsds, self.rhosds)
]
self.fluxsds = [
vsd * rhosd for vsd, rhosd in zip(self.vsds, self.rhosds)
]
self.vnsds = [
ufl.max_value(ufl.dot(vsd, self.n), 0) for vsd in self.vsds
]
self.facet_fluxsds = [
(vnsd('+') * ufl.max_value(rhosd('+'), 0.0) -
vnsd('-') * ufl.max_value(rhosd('-'), 0.0))
for vnsd, rhosd in zip(self.vnsds, self.rhosds)
]
#
# Now combine the subdomain fluxes to get the fluxes for
# the symmetrized functions
#
self.fluxs = matmul((2.0**-self.dim) * self.eomat, self.fluxsds)
self.facet_fluxs = matmul((2.0**-self.dim) * self.eomat,
self.facet_fluxsds)
self.rho_flux_jump = sum([
-facet_flux * ufl.jump(wrho) * self.dS
for facet_flux, wrho in zip(self.facet_fluxs, self.wrhos)
])
self.rho_grad_move = sum([
ufl.dot(flux, ufl.grad(wrho)) * self.dx
for flux, wrho in zip(self.fluxs, self.wrhos)
])
self.rho_penalty = sum([
-(self.degree**2 / self.havg) *
ufl.dot(ufl.jump(rho, self.n),
ufl.jump(self.rhopen * wrho, self.n)) * self.dS
for rho, wrho in zip(self.irhos, self.wrhos)
])
self.grho_penalty = sum([
self.degree**2 *
(ufl.jump(ufl.grad(rho), self.n) *
ufl.jump(ufl.grad(-self.grhopen * wrho), self.n)) * self.dS
for rho, wrho in zip(self.irhos, self.wrhos)
])
self.rho_terms = (self.rho_flux_jump + self.rho_grad_move +
self.rho_penalty + self.grho_penalty)
logVARIABLE('rho_terms made')
if not hasattr(self, 'U_terms'):
logVARIABLE('making U_terms')
self.Umin = self.iparams['Umin']
self.Upen = self.iparams['Upen']
self.gUpen = self.iparams['gUpen']
self.U_decay = 0.0
self.U_secretion = 0.0
self.jump_gUw = 0.0
self.U_diffusion = 0.0
self.U_penalty = 0.0
self.gU_penalty = 0.0
for j, lig in enumerate(self.iligands.ligands()):
sl = slice(j * 2**self.dim, (j + 1) * 2**self.dim)
self.U_decay += sum([
-lig.gamma * iUi * wUi * self.dx
for iUi, wUi in zip(self.iUs[sl], self.wUs[sl])
])
self.U_secretion += sum([
lig.s * rho * wU * self.dx
for rho, wU in zip(self.irhos, self.wUs[sl])
])
self.jump_gUw += sum([
ufl.jump(lig.D * wU * ufl.grad(U), self.n) * self.dS
for wU, U in zip(self.wUs[sl], self.iUs[sl])
])
self.U_diffusion += sum([
-lig.D * ufl.dot(ufl.grad(U), ufl.grad(wU)) * self.dx
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.U_penalty += sum([
(-self.degree**2 / self.havg) *
ufl.dot(ufl.jump(U, self.n),
ufl.jump(self.Upen * wU, self.n)) * self.dS
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.gU_penalty += sum([
-self.degree**2 * ufl.jump(ufl.grad(U), self.n) *
ufl.jump(ufl.grad(self.gUpen * wU), self.n) * self.dS
for U, wU in zip(self.iUs[sl], self.wUs[sl])
])
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty)
logVARIABLE('U_terms made')
if not hasattr(self, 'all_terms'):
logVARIABLE('making all_terms')
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
logVARIABLE('making J_terms')
self.J_terms = fe.derivative(self.all_terms, self.sol)
def setup_problem(self, t, debug=False):
self.set_time(t)
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
self.drho_integral = self.tdrho * self.wrho * self.dx
self.dU_integral = sum([
tdUi * wUi * self.dx for tdUi, wUi in zip(self.tdUs, self.wUs)
])
logVARIABLE('assembling A')
self.A = PETScMatrix()
logVARIABLE('self.A', self.A)
fe.assemble(self.drho_integral + self.dU_integral, tensor=self.A)
logVARIABLE('A assembled. Applying BCs')
self.dsol = Function(self.VS)
dsolsplit = self.dsol.split()
self.drho, self.dUs = dsolsplit[0], dsolsplit[1:]
#
# assemble RHS (for each time point, but compile only once)
#
if not hasattr(self, 'rho_terms'):
self.sigma = self.iparams['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rhomin = self.iparams['rhomin']
self.rhopen = self.iparams['rhopen']
self.grhopen = self.iparams['grhopen']
self.v = -ufl.grad(
self.V(self.iUs, ufl.max_value(self.irho, self.rhomin)) -
(self.s2 * ufl.grad(self.irho) /
ufl.max_value(self.irho, self.rhomin)))
self.flux = self.v * self.irho
self.vn = ufl.max_value(ufl.dot(self.v, self.n), 0)
self.facet_flux = ufl.jump(self.vn * ufl.max_value(self.irho, 0.0))
self.rho_flux_jump = -self.facet_flux * ufl.jump(
self.wrho) * self.dS
self.rho_grad_move = ufl.dot(self.flux, ufl.grad(
self.wrho)) * self.dx
self.rho_penalty = -(
(self.degree**2 / self.havg) *
ufl.dot(ufl.jump(self.irho, self.n),
ufl.jump(self.rhopen * self.wrho, self.n)) * self.dS)
self.grho_penalty = -(
self.degree**2 *
(ufl.jump(ufl.grad(self.irho), self.n) * ufl.jump(
ufl.grad(self.grhopen * self.wrho), self.n)) * self.dS)
self.rho_terms = (self.rho_flux_jump + self.rho_grad_move +
self.rho_penalty + self.grho_penalty)
if not hasattr(self, 'U_terms'):
self.Umin = self.iparams['Umin']
self.Upen = self.iparams['Upen']
self.gUpen = self.iparams['gUpen']
self.U_decay = sum([
-lig.gamma * iUi * wUi * self.dx for lig, iUi, wUi in zip(
self.iligands.ligands(), self.iUs, self.wUs)
])
self.U_secretion = sum([
lig.s * self.irho * wUi * self.dx
for lig, wUi in zip(self.iligands.ligands(), self.wUs)
])
self.jump_gUw = sum([
ufl.jump(lig.D * wUi * ufl.grad(iUi), self.n) * self.dS
for lig, wUi, iUi in zip(self.iligands.ligands(), self.wUs,
self.iUs)
])
self.U_diffusion = sum([
-lig.D * ufl.dot(ufl.grad(iUi), ufl.grad(wUi)) * self.dx
for lig, iUi, wUi in zip(self.iligands.ligands(), self.iUs,
self.wUs)
])
self.U_penalty = sum([
-(self.degree**2 / self.havg) * ufl.dot(
ufl.jump(iUi, self.n), ufl.jump(self.Upen * wUi, self.n)) *
self.dS for iUi, wUi in zip(self.iUs, self.wUs)
])
self.gU_penalty = sum([
-self.degree**2 * ufl.jump(ufl.grad(iUi), self.n) *
ufl.jump(ufl.grad(self.gUpen * wUi), self.n) * self.dS
for iUi, wUi in zip(self.iUs, self.wUs)
])
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty)
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
self.J_terms = fe.derivative(self.all_terms, self.sol)
def setup_problem(self, debug=False):
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
drho_integral = self.tdrho * self.wrho * self.dx
dU_integral = self.tdU * self.wU * self.dx
self.A = fe.assemble(drho_integral + dU_integral)
# if self.solver_type == 'lu':
# self.solver = fe.LUSolver(
# self.A,
# method=self.solver_type
# )
# self.solver.parameters['reuse_factorization'] = True
# else:
# self.solver = fe.KrylovSolver(
# self.A,
# self.solver_type,
# self.preconditioner_type
# )
self.dsol = Function(self.VS)
self.drho, self.dU = self.dsol.sub(0), self.dsol.sub(1)
#
# assemble RHS (has to be done for each time point)
#
if not hasattr(self, 'rho_terms'):
self.sigma = self.params['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rho_min = self.params['rho_min']
self.rhopen = self.params['rhopen']
self.grhopen = self.params['grhopen']
self.v = -ufl.grad(self.V(self.iU, self.irho))
self.flux = self.v * self.irho
self.vn = ufl.max_value(ufl.dot(self.v, self.n), 0)
self.facet_flux = (self.vn('+') * self.irho('+') -
self.vn('-') * self.irho('-'))
self.rho_flux_jump = -self.facet_flux * ufl.jump(
self.wrho) * self.dS
self.rho_grad_move = ufl.dot(self.flux, ufl.grad(
self.wrho)) * self.dx
self.rho_penalty = -(
(self.rhopen * self.degree**2 / self.havg) * ufl.dot(
ufl.jump(self.irho, self.n), ufl.jump(self.wrho, self.n)) *
self.dS)
# self.facet_flux = (
# self.vn('+')*self.rho('+') - self.vn('-')*self.rho('-')
# )
# self.rho_flux_jump = -self.facet_flux*ufl.jump(self.wrho)*self.dS
# self.rho_grad_move = ufl.dot(self.flux, ufl.grad(self.wrho))*self.dx
self.jump_grhow = (
self.s2 * ufl.jump(self.wrho * ufl.grad(self.irho), self.n) *
self.dS)
self.rho_diffusion = -self.s2 * ufl.dot(ufl.grad(
self.irho), ufl.grad(self.wrho)) * self.dx
# self.rho_penalty = -(
# (self.rhopen * self.degree**2 / self.havg) *
# ufl.dot(ufl.jump(self.rho, self.n),
# ufl.jump(self.wrho, self.n)) * self.dS
# )
self.grho_penalty = -(self.grhopen * self.degree**2 *
(ufl.jump(ufl.grad(self.irho), self.n) *
ufl.jump(ufl.grad(self.wrho), self.n)) *
self.dS)
self.rho_terms = (
# advection terms
self.rho_flux_jump + self.rho_grad_move +
# diffusive terms
self.rho_diffusion + self.jump_grhow +
# penalty terms (to enforce continuity)
self.rho_penalty + self.grho_penalty)
if not hasattr(self, 'U_terms'):
self.U_min = self.params['U_min']
self.gamma = self.params['gamma']
self.s = self.params['s']
self.D = self.params['D']
self.Upen = self.params['Upen']
self.gUpen = self.params['gUpen']
self.U_decay = -self.gamma * self.iU * self.wU * self.dx
self.U_secretion = self.s * self.irho * self.wU * self.dx
self.jump_gUw = (self.D *
ufl.jump(self.wU * ufl.grad(self.iU), self.n) *
self.dS)
self.U_diffusion = -self.D * ufl.dot(ufl.grad(self.iU),
ufl.grad(self.wU)) * self.dx
self.U_penalty = -(
(self.Upen * self.degree**2 / self.havg) *
ufl.dot(ufl.jump(self.iU, self.n), ufl.jump(self.wU, self.n)) *
self.dS)
self.gU_penalty = -(self.gUpen * self.degree**2 *
(ufl.jump(ufl.grad(self.iU), self.n) *
ufl.jump(ufl.grad(self.wU), self.n)) *
self.dS)
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty)
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
self.J_terms = fe.derivative(self.all_terms, self.sol)
def setup_problem(self, debug=False):
#
# assemble the matrix, if necessary (once for all time points)
#
if not hasattr(self, 'A'):
self.drho_integral = self.tdrho * self.wrho * self.dx
self.dU_integral = self.tdU * self.wU * self.dx
self.A = fe.assemble(self.drho_integral + self.dU_integral)
# if self.solver_type == 'lu':
# self.solver = fe.LUSolver(
# self.A,
# )
# self.solver.parameters['reuse_factorization'] = True
# else:
# self.solver = fe.KrylovSolver(
# self.A,
# self.solver_type,
# self.preconditioner_type
# )
# self.solver.parameters.add('linear_solver', self.solver_type)
# kparams = fe.Parameters('krylov_solver')
# kparams.add('report', True)
# kparams.add('nonzero_initial_guess', True)
# self.solver.parameters.add(kparams)
# lparams = fe.Parameters('lu_solver')
# lparams.add('report', True)
# lparams.add('reuse_factorization', True)
# lparams.add('verbose', True)
# self.solver.parameters.add(lparams)
self.dsol = Function(self.VS)
self.drho, self.dU = self.dsol.sub(0), self.dsol.sub(1)
#
# assemble RHS (for each time point, but compile only once)
#
if not hasattr(self, 'rho_terms'):
self.sigma = self.params['sigma']
self.s2 = self.sigma * self.sigma / 2
self.rho_min = self.params['rho_min']
self.rhopen = self.params['rhopen']
self.grhopen = self.params['grhopen']
self.v = -ufl.grad(self.V(self.iU, self.irho)) - (
self.s2 * ufl.grad(self.irho) /
ufl.max_value(self.irho, self.rho_min))
self.flux = self.v * self.irho
self.vn = ufl.max_value(ufl.dot(self.v, self.n), 0)
self.facet_flux = (
self.vn('+') * ufl.max_value(self.irho('+'), 0.0) -
self.vn('-') * ufl.max_value(self.irho('-'), 0.0))
self.rho_flux_jump = -self.facet_flux * ufl.jump(
self.wrho) * self.dS
self.rho_grad_move = ufl.dot(self.flux, ufl.grad(
self.wrho)) * self.dx
self.rho_penalty = -(
(self.rhopen * self.degree**2 / self.havg) * ufl.dot(
ufl.jump(self.irho, self.n), ufl.jump(self.wrho, self.n)) *
self.dS)
self.grho_penalty = -(self.grhopen * self.degree**2 *
(ufl.jump(ufl.grad(self.irho), self.n) *
ufl.jump(ufl.grad(self.wrho), self.n)) *
self.dS)
self.rho_terms = (self.rho_flux_jump + self.rho_grad_move +
self.rho_penalty + self.grho_penalty)
if not hasattr(self, 'U_terms'):
self.U_min = self.params['U_min']
self.gamma = self.params['gamma']
self.s = self.params['s']
self.D = self.params['D']
self.Upen = self.params['Upen']
self.gUpen = self.params['gUpen']
self.U_decay = -self.gamma * self.iU * self.wU * self.dx
self.U_secretion = self.s * self.irho * self.wU * self.dx
self.jump_gUw = (self.D *
ufl.jump(self.wU * ufl.grad(self.iU), self.n) *
self.dS)
self.U_diffusion = -self.D * ufl.dot(ufl.grad(self.iU),
ufl.grad(self.wU)) * self.dx
self.U_penalty = -(
(self.Upen * self.degree**2 / self.havg) *
ufl.dot(ufl.jump(self.iU, self.n), ufl.jump(self.wU, self.n)) *
self.dS)
self.gU_penalty = -(self.gUpen * self.degree**2 *
(ufl.jump(ufl.grad(self.iU), self.n) *
ufl.jump(ufl.grad(self.wU), self.n)) *
self.dS)
self.U_terms = (
# decay and secretion
self.U_decay + self.U_secretion +
# diffusion
self.jump_gUw + self.U_diffusion +
# penalties (to enforce continuity)
self.U_penalty + self.gU_penalty)
if not hasattr(self, 'all_terms'):
self.all_terms = self.rho_terms + self.U_terms
if not hasattr(self, 'J_terms'):
self.J_terms = fe.derivative(self.all_terms, self.sol)
def boundary_R(x, on_boundary):
return on_boundary and near(x[0], 1)
bc_R = DirichletBC(V, p_R, boundary_R)
bcs = [bc_L, bc_R]
# Defining variational problem
p = TrialFunction(V)
v = TestFunction(V)
d = 2
I = Identity(d)
x, y = SpatialCoordinate(mesh)
M = max_value(Constant(0.10), exp(-(10 * y - 1.0 * sin(10 * x) - 5.0)**2))
K = M * I
a = dot(K * grad(p), grad(v)) * dx
f1 = as_vector((-2 * x, 0))
f = nabla_div(dot(-K, f1))
L = inner(f, v) * dx
# Computing solutions
p = Function(V)
solve(a == L, p, bcs)
u_bar = -K * grad(p)
# Projecting the Velocity profile
W = VectorFunctionSpace(mesh, 'P', 1)
u_bar1 = project(u_bar, W)