/usr/lib/python2.7/dist-packages/ffc/errorcontrol/errorcontrolgenerators.py is in python-ffc 1.4.0-1.
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This module provides an abstract ErrorControlGenerator class for
generating forms required for goal-oriented error control and a
realization of this: UFLErrorControlGenerator for handling pure UFL
forms.
"""
# Copyright (C) 2010 Marie E. Rognes
#
# This file is part of FFC.
#
# FFC is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FFC 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 FFC. If not, see <http://www.gnu.org/licenses/>.
#
# Last changed: 2011-06-29
from ufl import inner, dx, ds, dS, avg, replace, action
from ufl.algorithms.analysis import extract_arguments
__all__ = ["ErrorControlGenerator", "UFLErrorControlGenerator"]
class ErrorControlGenerator:
def __init__(self, module, F, M, u):
"""
*Arguments*
module (Python module)
The module to use for specific form manipulations
(typically ufl or dolfin)
F (tuple or Form)
tuple of (bilinear, linear) forms or linear form
M (Form)
functional or linear form
u (Coefficient)
The coefficient considered as the unknown.
"""
# Store module
self.module = module
# Store solution Coefficient/Function
self.u = u
# Extract the lhs (bilinear form), rhs (linear form), goal
# (functional), weak residual (linear form)
linear_case = (isinstance(F, (tuple, list)) and len(F) == 2)
if linear_case:
self.lhs, self.rhs = F
try:
self.goal = action(M, u)
except:
self.goal = M # Allow functionals as input as well
self.weak_residual = self.rhs - action(self.lhs, u)
else:
self.lhs = self.module.derivative(F, u)
self.rhs = F
self.goal = M
self.weak_residual = - F
# At least check that final forms have correct rank
assert(len(extract_arguments(self.lhs)) == 2)
assert(len(extract_arguments(self.rhs)) == 1)
assert(len(extract_arguments(self.goal)) == 0)
assert(len(extract_arguments(self.weak_residual)) == 1)
# Get the domain, assuming there's only one
assert(len(self.weak_residual.domains()) == 1)
self.domain, = self.weak_residual.domains()
# Store map from identifiers to names for forms and generated
# coefficients
self.ec_names = {}
# Use predefined names for the forms in the primal problem
self.ec_names[id(self.lhs)] = "lhs"
self.ec_names[id(self.rhs)] = "rhs"
self.ec_names[id(self.goal)] = "goal"
# Initialize other required data
self.initialize_data()
def initialize_data(self):
"""
Initialize specific data
"""
msg = """ErrorControlGenerator acts as an abstract
class. Subclasses must overload the initialize_data() method
and provide a certain set of variables. See
UFLErrorControlGenerator for an example."""
raise NotImplementedError, msg
def generate_all_error_control_forms(self):
"""
Utility function for generating all (8) forms required for
error control in addition to the primal forms
"""
# Generate dual forms
(a_star, L_star) = self.dual_forms()
# Generate forms for computing strong cell residual
(a_R_T, L_R_T) = self.cell_residual()
# Generate forms for computing strong facet residuals
(a_R_dT, L_R_dT) = self.facet_residual()
# Generate form for computing error estimate
eta_h = self.error_estimate()
# Generate form for computing error indicators
eta_T = self.error_indicators()
# Paranoid checks added after introduction of multidomain features in ufl:
for i, form in enumerate((a_star, L_star, eta_h, a_R_T, L_R_T, a_R_dT, L_R_dT, eta_T)):
assert len(form.domains()) > 0, ("Zero domains at form %d" % i)
assert len(form.domains()) == 1, ("%d domains at form %d" % (len(form.domains()), i))
# Return all generated forms in CERTAIN order matching
# constructor of dolfin/adaptivity/ErrorControl.h
return (a_star, L_star, eta_h, a_R_T, L_R_T, a_R_dT, L_R_dT, eta_T)
def primal_forms(self):
"""
Return primal forms in order (bilinear, linear, functional)
"""
return self.lhs, self.rhs, self.goal
def dual_forms(self):
"""
Generate and return (bilinear, linear) forms defining linear
dual variational problem
"""
a_star = self.module.adjoint(self.lhs)
L_star = self.module.derivative(self.goal, self.u)
return (a_star, L_star)
def cell_residual(self):
"""
Generate and return (bilinear, linear) forms defining linear
variational problem for the strong cell residual
"""
# Define trial and test functions for the cell residuals on
# discontinuous version of primal trial space
R_T = self.module.TrialFunction(self._dV)
v = self.module.TestFunction(self._dV)
# Extract original test function in the weak residual
v_h = extract_arguments(self.weak_residual)[0]
# Define forms defining linear variational problem for cell
# residual
v_T = self._b_T*v
a_R_T = inner(v_T, R_T)*dx(self.domain)
L_R_T = replace(self.weak_residual, {v_h: v_T})
return (a_R_T, L_R_T)
def facet_residual(self):
"""
Generate and return (bilinear, linear) forms defining linear
variational problem for the strong facet residual(s)
"""
# Define trial and test functions for the facet residuals on
# discontinuous version of primal trial space
R_e = self.module.TrialFunction(self._dV)
v = self.module.TestFunction(self._dV)
# Extract original test function in the weak residual
v_h = extract_arguments(self.weak_residual)[0]
# Define forms defining linear variational problem for facet
# residual
v_e = self._b_e*v
a_R_dT = ((inner(v_e('+'), R_e('+')) + inner(v_e('-'), R_e('-')))*dS(self.domain)
+ inner(v_e, R_e)*ds(self.domain))
L_R_dT = (replace(self.weak_residual, {v_h: v_e})
- inner(v_e, self._R_T)*dx(self.domain))
return (a_R_dT, L_R_dT)
def error_estimate(self):
"""
Generate and return functional defining error estimate
"""
# Error estimate defined as r(Ez_h):
eta_h = action(self.weak_residual, self._Ez_h)
return eta_h
def error_indicators(self):
"""
Generate and return linear form defining error indicators
"""
# Extract these to increase readability
R_T = self._R_T
R_dT = self._R_dT
z = self._Ez_h
z_h = self._z_h
# Define linear form for computing error indicators
v = self.module.TestFunction(self._DG0)
eta_T = (v*inner(R_T, z - z_h)*dx(self.domain)
+ avg(v)*(inner(R_dT('+'), (z - z_h)('+'))
+ inner(R_dT('-'), (z - z_h)('-')))*dS(self.domain)
+ v*inner(R_dT, z - z_h)*ds(self.domain))
return eta_T
class UFLErrorControlGenerator(ErrorControlGenerator):
"""
This class provides a realization of ErrorControlGenerator for use
with pure UFL forms
"""
def __init__(self, F, M, u):
"""
*Arguments*
F (tuple or Form)
tuple of (bilinear, linear) forms or linear form
M (Form)
functional or linear form
u (Coefficient)
The coefficient considered as the unknown.
"""
ErrorControlGenerator.__init__(self, __import__("ufl"), F, M, u)
def initialize_data(self):
"""
Extract required objects for defining error control
forms. This will be stored, reused and in particular named.
"""
# Developer's note: The UFL-FFC-DOLFIN--PyDOLFIN toolchain for
# error control is quite fine-tuned. In particular, the order
# of coefficients in forms is (and almost must be) used for
# their assignment. This means that the order in which these
# coefficients are defined matters and should be considered
# fixed.
from ufl import FiniteElement, Coefficient
from ufl.algorithms.elementtransformations import tear, increase_order
# Primal trial element space
self._V = self.u.element()
# Primal test space == Dual trial space
Vhat = extract_arguments(self.weak_residual)[0].element()
# Discontinuous version of primal trial element space
self._dV = tear(self._V)
# Extract domain and geometric dimension
domain, = self._V.domains()
gdim = domain.geometric_dimension()
# Coefficient representing improved dual
E = increase_order(Vhat)
self._Ez_h = Coefficient(E)
self.ec_names[id(self._Ez_h)] = "__improved_dual"
# Coefficient representing cell bubble function
B = FiniteElement("B", domain, gdim + 1)
self._b_T = Coefficient(B)
self.ec_names[id(self._b_T)] = "__cell_bubble"
# Coefficient representing strong cell residual
self._R_T = Coefficient(self._dV)
self.ec_names[id(self._R_T)] = "__cell_residual"
# Coefficient representing cell cone function
C = FiniteElement("DG", domain, gdim)
self._b_e = Coefficient(C)
self.ec_names[id(self._b_e)] = "__cell_cone"
# Coefficient representing strong facet residual
self._R_dT = Coefficient(self._dV)
self.ec_names[id(self._R_dT)] = "__facet_residual"
# Define discrete dual on primal test space
self._z_h = Coefficient(Vhat)
self.ec_names[id(self._z_h)] = "__discrete_dual_solution"
# Piecewise constants for assembling indicators
self._DG0 = FiniteElement("DG", domain, 0)
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