#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2020 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
"""Simplified version of the thermalblock demo.
Usage:
thermalblock_simple.py MODEL ALG SNAPSHOTS RBSIZE TEST
Arguments:
"""
from typer import Argument, run
from pymor.basic import * # most common pyMOR functions and classes
from pymor.tools.typer import Choices
# parameters for high-dimensional models
XBLOCKS = 2 # pyMOR/FEniCS
YBLOCKS = 2 # pyMOR/FEniCS
GRID_INTERVALS = 100 # pyMOR/FEniCS
FENICS_ORDER = 2
NGS_ORDER = 4
TEXT = 'pyMOR'
####################################################################################################
# Main script #
####################################################################################################
[docs]def main(
model: Choices('pymor fenics ngsolve pymor_text') = Argument(..., help='High-dimensional model.'),
alg: Choices('naive greedy adaptive_greedy pod') = Argument(..., help='The model reduction algorithm to use.'),
snapshots: int = Argument(
...,
help='naive: ignored.\n\n'
'greedy/pod: Number of training_set parameters per block'
'(in total SNAPSHOTS^(XBLOCKS * YBLOCKS) parameters).\n\n'
'adaptive_greedy: size of validation set.'
),
rbsize: int = Argument(..., help='Size of the reduced basis.'),
test: int = Argument(..., help='Number of parameters for stochastic error estimation.'),
):
# discretize
############
if model == 'pymor':
fom, parameter_space = discretize_pymor()
elif model == 'fenics':
fom, parameter_space = discretize_fenics()
elif model == 'ngsolve':
fom, parameter_space = discretize_ngsolve()
elif model == 'pymor_text':
fom, parameter_space = discretize_pymor_text()
else:
raise NotImplementedError
# select reduction algorithm with error estimator
#################################################
coercivity_estimator = ExpressionParameterFunctional('min(diffusion)', fom.parameters)
reductor = CoerciveRBReductor(fom, product=fom.h1_0_semi_product, coercivity_estimator=coercivity_estimator,
check_orthonormality=False)
# generate reduced model
########################
if alg == 'naive':
rom = reduce_naive(fom, reductor, parameter_space, rbsize)
elif alg == 'greedy':
rom = reduce_greedy(fom, reductor, parameter_space, snapshots, rbsize)
elif alg == 'adaptive_greedy':
rom = reduce_adaptive_greedy(fom, reductor, parameter_space, snapshots, rbsize)
elif alg == 'pod':
rom = reduce_pod(fom, reductor, parameter_space, snapshots, rbsize)
else:
raise NotImplementedError
# evaluate the reduction error
##############################
results = reduction_error_analysis(rom, fom=fom, reductor=reductor, error_estimator=True,
error_norms=[fom.h1_0_semi_norm], condition=True,
test_mus=parameter_space.sample_randomly(test),
plot=True)
# show results
##############
print(results['summary'])
import matplotlib.pyplot
matplotlib.pyplot.show()
# write results to disk
#######################
from pymor.core.pickle import dump
dump((rom, parameter_space), open('reduced_model.out', 'wb'))
results.pop('figure') # matplotlib figures cannot be serialized
dump(results, open('results.out', 'wb'))
# visualize reduction error for worst-approximated mu
#####################################################
mumax = results['max_error_mus'][0, -1]
U = fom.solve(mumax)
U_RB = reductor.reconstruct(rom.solve(mumax))
fom.visualize((U, U_RB, U - U_RB), legend=('Detailed Solution', 'Reduced Solution', 'Error'),
separate_colorbars=True, block=True)
####################################################################################################
# High-dimensional models #
####################################################################################################
[docs]def discretize_pymor():
# setup analytical problem
problem = thermal_block_problem(num_blocks=(XBLOCKS, YBLOCKS))
# discretize using continuous finite elements
fom, _ = discretize_stationary_cg(problem, diameter=1. / GRID_INTERVALS)
return fom, problem.parameter_space
[docs]def discretize_fenics():
from pymor.tools import mpi
if mpi.parallel:
from pymor.models.mpi import mpi_wrap_model
fom = mpi_wrap_model(_discretize_fenics, use_with=True, pickle_local_spaces=False)
else:
fom = _discretize_fenics()
return fom, fom.parameters.space((0.1, 1))
def _discretize_fenics():
# assemble system matrices - FEniCS code
########################################
import dolfin as df
mesh = df.UnitSquareMesh(GRID_INTERVALS, GRID_INTERVALS, 'crossed')
V = df.FunctionSpace(mesh, 'Lagrange', FENICS_ORDER)
u = df.TrialFunction(V)
v = df.TestFunction(V)
diffusion = df.Expression('(lower0 <= x[0]) * (open0 ? (x[0] < upper0) : (x[0] <= upper0)) *'
'(lower1 <= x[1]) * (open1 ? (x[1] < upper1) : (x[1] <= upper1))',
lower0=0., upper0=0., open0=0,
lower1=0., upper1=0., open1=0,
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
def assemble_matrix(x, y, nx, ny):
diffusion.user_parameters['lower0'] = x/nx
diffusion.user_parameters['lower1'] = y/ny
diffusion.user_parameters['upper0'] = (x + 1)/nx
diffusion.user_parameters['upper1'] = (y + 1)/ny
diffusion.user_parameters['open0'] = (x + 1 == nx)
diffusion.user_parameters['open1'] = (y + 1 == ny)
return df.assemble(df.inner(diffusion * df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
mats = [assemble_matrix(x, y, XBLOCKS, YBLOCKS)
for x in range(XBLOCKS) for y in range(YBLOCKS)]
mat0 = mats[0].copy()
mat0.zero()
h1_mat = df.assemble(df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
f = df.Constant(1.) * v * df.dx
F = df.assemble(f)
bc = df.DirichletBC(V, 0., df.DomainBoundary())
for m in mats:
bc.zero(m)
bc.apply(mat0)
bc.apply(h1_mat)
bc.apply(F)
# wrap everything as a pyMOR model
##################################
# FEniCS wrappers
from pymor.bindings.fenics import FenicsVectorSpace, FenicsMatrixOperator, FenicsVisualizer
# define parameter functionals (same as in pymor.analyticalproblems.thermalblock)
parameter_functionals = [ProjectionParameterFunctional('diffusion',
size=YBLOCKS*XBLOCKS,
index=YBLOCKS - y - 1 + x*YBLOCKS)
for x in range(XBLOCKS) for y in range(YBLOCKS)]
# wrap operators
ops = [FenicsMatrixOperator(mat0, V, V)] + [FenicsMatrixOperator(m, V, V) for m in mats]
op = LincombOperator(ops, [1.] + parameter_functionals)
rhs = VectorOperator(FenicsVectorSpace(V).make_array([F]))
h1_product = FenicsMatrixOperator(h1_mat, V, V, name='h1_0_semi')
# build model
visualizer = FenicsVisualizer(FenicsVectorSpace(V))
fom = StationaryModel(op, rhs, products={'h1_0_semi': h1_product},
visualizer=visualizer)
return fom
[docs]def discretize_ngsolve():
from ngsolve import (ngsglobals, Mesh, H1, CoefficientFunction, LinearForm, SymbolicLFI,
BilinearForm, SymbolicBFI, grad, TaskManager)
from netgen.csg import CSGeometry, OrthoBrick, Pnt
import numpy as np
ngsglobals.msg_level = 1
geo = CSGeometry()
obox = OrthoBrick(Pnt(-1, -1, -1), Pnt(1, 1, 1)).bc("outer")
b = []
b.append(OrthoBrick(Pnt(-1, -1, -1), Pnt(0.0, 0.0, 0.0)).mat("mat1").bc("inner"))
b.append(OrthoBrick(Pnt(-1, 0, -1), Pnt(0.0, 1.0, 0.0)).mat("mat2").bc("inner"))
b.append(OrthoBrick(Pnt(0, -1, -1), Pnt(1.0, 0.0, 0.0)).mat("mat3").bc("inner"))
b.append(OrthoBrick(Pnt(0, 0, -1), Pnt(1.0, 1.0, 0.0)).mat("mat4").bc("inner"))
b.append(OrthoBrick(Pnt(-1, -1, 0), Pnt(0.0, 0.0, 1.0)).mat("mat5").bc("inner"))
b.append(OrthoBrick(Pnt(-1, 0, 0), Pnt(0.0, 1.0, 1.0)).mat("mat6").bc("inner"))
b.append(OrthoBrick(Pnt(0, -1, 0), Pnt(1.0, 0.0, 1.0)).mat("mat7").bc("inner"))
b.append(OrthoBrick(Pnt(0, 0, 0), Pnt(1.0, 1.0, 1.0)).mat("mat8").bc("inner"))
box = (obox - b[0] - b[1] - b[2] - b[3] - b[4] - b[5] - b[6] - b[7])
geo.Add(box)
for bi in b:
geo.Add(bi)
# domain 0 is empty!
mesh = Mesh(geo.GenerateMesh(maxh=0.3))
# H1-conforming finite element space
V = H1(mesh, order=NGS_ORDER, dirichlet="outer")
v = V.TestFunction()
u = V.TrialFunction()
# Coeff as array: variable coefficient function (one CoefFct. per domain):
sourcefct = CoefficientFunction([1 for i in range(9)])
with TaskManager():
# the right hand side
f = LinearForm(V)
f += SymbolicLFI(sourcefct * v)
f.Assemble()
# the bilinear-form
mats = []
coeffs = [[0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 0, 0, 0]]
for c in coeffs:
diffusion = CoefficientFunction(c)
a = BilinearForm(V, symmetric=False)
a += SymbolicBFI(diffusion * grad(u) * grad(v), definedon=(np.where(np.array(c) == 1)[0] + 1).tolist())
a.Assemble()
mats.append(a.mat)
from pymor.bindings.ngsolve import NGSolveVectorSpace, NGSolveMatrixOperator, NGSolveVisualizer
space = NGSolveVectorSpace(V)
op = LincombOperator([NGSolveMatrixOperator(m, space, space) for m in mats],
[ProjectionParameterFunctional('diffusion', len(coeffs), i) for i in range(len(coeffs))])
h1_0_op = op.assemble(Mu(diffusion=[1] * len(coeffs))).with_(name='h1_0_semi')
F = space.zeros()
F._list[0].real_part.impl.vec.data = f.vec
F = VectorOperator(F)
fom = StationaryModel(op, F, visualizer=NGSolveVisualizer(mesh, V),
products={'h1_0_semi': h1_0_op})
return fom, fom.parameters.space((0.1, 1))
[docs]def discretize_pymor_text():
# setup analytical problem
problem = text_problem(TEXT)
# discretize using continuous finite elements
fom, _ = discretize_stationary_cg(problem, diameter=1.)
return fom, problem.parameter_space
####################################################################################################
# Reduction algorithms #
####################################################################################################
[docs]def reduce_naive(fom, reductor, parameter_space, basis_size):
training_set = parameter_space.sample_randomly(basis_size)
for mu in training_set:
reductor.extend_basis(fom.solve(mu), method='trivial')
rom = reductor.reduce()
return rom
[docs]def reduce_greedy(fom, reductor, parameter_space, snapshots, basis_size):
training_set = parameter_space.sample_uniformly(snapshots)
pool = new_parallel_pool()
greedy_data = rb_greedy(fom, reductor, training_set,
extension_params={'method': 'gram_schmidt'},
max_extensions=basis_size,
pool=pool)
return greedy_data['rom']
[docs]def reduce_adaptive_greedy(fom, reductor, parameter_space, validation_mus, basis_size):
pool = new_parallel_pool()
greedy_data = rb_adaptive_greedy(fom, reductor, parameter_space,
validation_mus=-validation_mus,
extension_params={'method': 'gram_schmidt'},
max_extensions=basis_size,
pool=pool)
return greedy_data['rom']
[docs]def reduce_pod(fom, reductor, parameter_space, snapshots, basis_size):
training_set = parameter_space.sample_uniformly(snapshots)
snapshots = fom.operator.source.empty()
for mu in training_set:
snapshots.append(fom.solve(mu))
basis, singular_values = pod(snapshots, modes=basis_size, product=reductor.products['RB'])
reductor.extend_basis(basis, method='trivial')
rom = reductor.reduce()
return rom
if __name__ == '__main__':
run(main)