#
# RBniCS is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RBniCS. If not, see <http://www.gnu.org/licenses/>.
#
import hashlib
from rbnics.backends import assign, copy, Function, LinearSolver, product, sum, transpose
from rbnics.problems.base import LinearProblem, ParametrizedDifferentialProblem
from rbnics.utils.cache import Cache
StokesOptimalControlProblem_Base = LinearProblem(
ParametrizedDifferentialProblem)
class StokesOptimalControlProblem(StokesOptimalControlProblem_Base):
"""
The problem to be solved is
min {J(y, u) = 1/2 m(v - v_d, v - v_d) + 1/2 n(u, u)}
y = (v, p) in Y = (V, P), u in U
s.t.
a(v, phi) + b(phi, p) = c(u, phi) + <f, phi> for all phi in V
b(v, xi) = <l, xi> for all xi in P
This class will solve the following optimality conditions:
m(v, psi) + a*(psi, w) + b*(psi, q) = <g, psi> for all psi in V
b*(w, pi ) = 0 for all pi in P
n(u, tau) - c*(tau, w) = 0 for all tau in U
# Copyright (C) 2015-2020 by the RBniCS authors
#
# This file is part of RBniCS.
#
# SPDX-License-Identifier: LGPL-3.0-or-later
from rbnics.problems.base import LinearProblem, ParametrizedDifferentialProblem
from rbnics.backends import product, sum, transpose
EllipticProblem_Base = LinearProblem(ParametrizedDifferentialProblem)
# Base class containing the definition of elliptic problems
class EllipticProblem(EllipticProblem_Base):
# Default initialization of members
def __init__(self, V, **kwargs):
# Call to parent
EllipticProblem_Base.__init__(self, V, **kwargs)
# Form names for elliptic problems
self.terms = ["a", "f", "s"]
self.terms_order = {"a": 2, "f": 1, "s": 1}
self.components = ["u"]
class ProblemSolver(EllipticProblem_Base.ProblemSolver):
def matrix_eval(self):
problem = self.problem
return sum(
product(problem.compute_theta("a"), problem.operator["a"]))
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RBniCS is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RBniCS. If not, see <http://www.gnu.org/licenses/>.
#
from rbnics.problems.base import LinearProblem, ParametrizedDifferentialProblem
from rbnics.backends import product, sum
GeostrophicProblem_Base = LinearProblem(ParametrizedDifferentialProblem)
class GeostrophicProblem(GeostrophicProblem_Base):
# Default initialization of members
def __init__(self, V, **kwargs):
# Call to parent
GeostrophicProblem_Base.__init__(self, V, **kwargs)
# Form names for geostrophic problems
self.terms = ["a", "f"]
self.terms_order = {"a": 2, "f": 1}
self.components = ["psi", "q"]
# Perform a truth solve
class ProblemSolver(GeostrophicProblem_Base.ProblemSolver):
#
# RBniCS is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RBniCS. If not, see <http://www.gnu.org/licenses/>.
#
import hashlib
from rbnics.problems.base import LinearProblem, ParametrizedDifferentialProblem
from rbnics.backends import assign, copy, Function, LinearSolver, product, sum
from rbnics.utils.cache import Cache
StokesProblem_Base = LinearProblem(ParametrizedDifferentialProblem)
# Base class containing the definition of saddle point problems
class StokesProblem(StokesProblem_Base):
# Default initialization of members
def __init__(self, V, **kwargs):
# Call to parent
StokesProblem_Base.__init__(self, V, **kwargs)
# Form names for saddle point problems
self.terms = [
"a", "b", "bt", "f", "g",
# Auxiliary terms for supremizer enrichment
"bt_restricted"
]
# Copyright (C) 2015-2021 by the RBniCS authors
#
# This file is part of RBniCS.
#
# SPDX-License-Identifier: LGPL-3.0-or-later
from rbnics.problems.base import LinearProblem, ParametrizedDifferentialProblem
from rbnics.backends import product, sum, transpose
GeostrophicOptimalControlProblem_Base = LinearProblem(ParametrizedDifferentialProblem)
class GeostrophicOptimalControlProblem(GeostrophicOptimalControlProblem_Base):
"""
The problem to be solved is
min {J(y_psi, u) = 1/2 m(y_psi - y_d, y_psi - y_d) + 1/2 n(u, u)}
(y_psi, y_q) in YxY, y_d in Y, u in U
s.t.
a((y_psi, y_q), (z_psi, z_q)) = c(u, z_psi) + <f, z_q> for all (z_psi, z_q) in YxY
This class will solve the following optimality conditions:
m(y_psi, z_q) + a*((p_psi, p_q), (z_psi, z_q)) = <g, z_q> for all (z_psi, z_q) in YxY
n(u, v) - c*(v, ppsi) = 0 for all v in U
a((y_psi, y_q), (q_psi, q_q))- c(u, q_psi) = <f, q_q> for all (q_psi, q_q) in YxY
and compute the cost functional
J(y_psi, u) = 1/2 m(y_psi, y_psi) + 1/2 n(u, u) - <g, y_psi> + 1/2 h
where
a*(., .) is the adjoint of a