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mixed_problem_engine_base.py
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Wed, Jan 29, 04:44

mixed_problem_engine_base.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy 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.
#
# RROMPy 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 RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import numpy as np
import fenics as fen
from scipy.sparse import csr_matrix
from matplotlib import pyplot as plt
from rrompy.utilities.base.types import Np1D, strLst
from .problem_engine_base import ProblemEngineBase
from rrompy.utilities.base import purgeList, getNewFilename, verbosityDepth
__all__ = ['MixedProblemEngineBase']
class MixedProblemEngineBase(ProblemEngineBase):
"""
Generic solver for parametric mixed problems.
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real mixed FE space.
u: Generic mixed trial functions for variational form evaluation.
v: Generic mixed test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
bsmu: Mu value of last bs evaluation.
liftDirichletDatamu: Mu value of last Dirichlet datum evaluation.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
"""
nAs, nbs = 1, 1
functional = lambda self, u: 0.
def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity)
V1 = fen.FiniteElement("P", fen.triangle, 1)
V2 = fen.FiniteElement("R", fen.triangle, 0)
element = fen.MixedElement([V1, V2])
self.V = fen.FunctionSpace(fen.UnitSquareMesh(10, 10), element)
self.primalIndices = [0]
def buildEnergyNormForm(self): # L2 primal
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling energy matrix.", end = "")
a = 0.
for j in self.primalIndices:
a = a + fen.dot(self.u[j], self.v[j])
normMatFen = fen.assemble(a * fen.dx)
normMat = fen.as_backend_type(normMatFen).mat()
self.energyNormMatrix = csr_matrix(normMat.getValuesCSR()[::-1],
shape = normMat.size)
if self.verbosity >= 20:
verbosityDepth("DEL", " Done.", inline = True)
def plot(self, u:Np1D, name : strLst = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, **figspecs):
"""
Do some nice plots of the complex-valued function with given dofs.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
if isinstance(what, (str,)):
if what.upper() == 'ALL':
what = ['ABS', 'PHASE', 'REAL', 'IMAG']
else:
what = [what]
what = purgeList(what, ['ABS', 'PHASE', 'REAL', 'IMAG'],
listname = self.name() + ".what", baselevel = 1)
if len(what) == 0: return
if 'figsize' not in figspecs.keys():
figspecs['figsize'] = (13. * len(what) / 4, 3)
if isinstance(name, (str,)):
name = ["{}_sub{}".format(name, j + 1)\
for j in range(self.V.num_sub_spaces())]
for j in range(self.V.num_sub_spaces()):
subplotcode = 100 + len(what) * 10
Vj = self.V.sub(j)
dofs = Vj.dofmap().dofs()
uj = u[dofs]
plt.figure(**figspecs)
Vj = Vj.collapse()
plt.jet()
if 'ABS' in what:
uAb = fen.Function(Vj)
uAb.vector()[:] = np.array(np.abs(uj), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uAb, title = "|{}|".format(name[j]))
plt.colorbar(p)
if 'PHASE' in what:
uPh = fen.Function(Vj)
uPh.vector()[:] = np.array(np.angle(uj), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uPh, title = "phase({})".format(name[j]))
plt.colorbar(p)
if 'REAL' in what:
uRe = fen.Function(Vj)
uRe.vector()[:] = np.array(np.real(uj), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uRe, title = "Re({})".format(name[j]))
plt.colorbar(p)
if 'IMAG' in what:
uIm = fen.Function(Vj)
uIm.vector()[:] = np.array(np.imag(uj), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uIm, title = "Im({})".format(name[j]))
plt.colorbar(p)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_sub{}_fig_".format(save, j + 1),
saveFormat),
format = saveFormat, dpi = saveDPI)
plt.show()
plt.close()

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