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__init__.py
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# -*- mode:python; coding: utf-8 -*-
#
# Copyright (©) 2016-2023 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
# Copyright (©) 2020-2023 Lucas Frérot
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program 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 Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
"""Nonlinear solvers for plasticity problems.
Solvers in this module use :py:mod:`scipy.optimize` to solve the implicit
non-linear equation for plastic deformations with fixed contact pressures.
"""
import numpy as np
from functools import wraps
from scipy.optimize import newton_krylov, root
from scipy.sparse.linalg import bicgstab, LinearOperator
from .._tamaas import (
EPSolver,
Logger,
LogLevel,
mpi,
_tolerance_manager,
_DFSANESolver as DFSANECXXSolver,
)
__all__ = ['NLNoConvergence',
'DFSANESolver',
'DFSANECXXSolver',
'NewtonKrylovSolver',
'ToleranceManager']
class NLNoConvergence(RuntimeError):
"""Convergence not reached exception."""
class NewtonRaphsonSolver(EPSolver):
"""Basic Newton-Raphson scheme"""
def __init__(self, residual):
super(NewtonRaphsonSolver, self).__init__(residual)
self._x = self.getStrainIncrement()
self._residual = self.getResidual()
self.max_iter = 1000
def solve(self):
EPSolver.beforeSolve(self)
# assemble RHS
self._residual.computeResidual(self._x)
rhs = -self._residual.vector.ravel()
norm_0 = np.linalg.norm(rhs) / rhs.size
if norm_0 < self.tolerance:
Logger().get(LogLevel.info) << (
"NewtonRaphson: successful convergence (0 iterations,"
f" {self.tolerance}, {norm_0})\n")
self._residual.computeResidualDisplacement(self._x)
return
# define linear operator
def residual_tangent(x):
v = np.zeros_like(x)
self._residual.applyTangent(v, x, self._x)
return v.ravel()
T = LinearOperator(matvec=residual_tangent, shape=[self._x.size] * 2)
error = norm_0
nit = 0
while error > self.tolerance and nit < self.max_iter:
self._residual.computeResidual(self._x)
rhs = -self._residual.vector.ravel()
x, error_code = bicgstab(T, rhs, atol=1e-10)
self._x += x.reshape(self._x.shape)
error = np.linalg.norm(rhs) / rhs.size
nit += 1
if error > self.tolerance:
msg = "did not converge"
else:
msg = "successful convergence"
Logger().get(LogLevel.info) << (
f"NewtonRaphson: {msg} ({nit} iterations,"
f" {self.tolerance}, {error:.3e})\n")
self._residual.computeResidualDisplacement(self._x)
class ScipySolver(EPSolver):
"""Base class for solvers wrapping SciPy routines."""
def __init__(self, residual, model=None, callback=None):
"""Construct nonlinear solver with residual.
:param residual: plasticity residual object
:param model: Deprecated
:param callback: passed on to the Scipy solver
"""
super(ScipySolver, self).__init__(residual)
if mpi.size() > 1:
raise RuntimeError("Scipy solvers cannot be used with MPI; "
"DFSANECXXSolver can be used instead")
self.callback = callback
self._x = self.getStrainIncrement()
self._residual = self.getResidual()
self.options = {'ftol': 0, 'fatol': 1e-9}
def solve(self):
"""Solve R(δε) = 0 using a Scipy function."""
# For initial guess, compute the strain due to boundary tractions
# self._residual.computeResidual(self._x)
# self._x[...] = self._residual.getVector()
EPSolver.beforeSolve(self)
# Scipy root callback
def compute_residual(vec):
self._residual.computeResidual(vec)
return self._residual.vector.copy()
# Solve
Logger().get(LogLevel.debug) << \
"Entering non-linear solve\n"
self._x[...] = self._scipy_solve(compute_residual)
Logger().get(LogLevel.debug) << \
"Non-linear solve returned"
# Computing displacements
self._residual.computeResidualDisplacement(self._x)
def reset(self):
"""Set solution vector to zero."""
self._x[...] = 0
def _scipy_solve(self, compute_residual):
"""Actually call the scipy solver.
:param compute_residual: function returning residual for given variable
"""
raise NotImplementedError()
class NewtonKrylovSolver(ScipySolver):
"""Solve using a finite-difference Newton-Krylov method."""
def _scipy_solve(self, compute_residual):
try:
return newton_krylov(compute_residual, self._x,
f_tol=self.tolerance,
verbose=False, callback=self.callback)
except Exception:
raise NLNoConvergence("Newton-Krylov did not converge")
class DFSANESolver(ScipySolver):
"""Solve using a spectral residual jacobianless method.
See :doi:`10.1090/S0025-5718-06-01840-0` for details on method and
the relevant Scipy `documentation
<https://scipy.github.io/devdocs/reference/optimize.root-dfsane.html>`_ for
details on parameters.
"""
def _scipy_solve(self, compute_residual):
solution = root(compute_residual,
self._x,
method='df-sane',
options={'ftol': 0, 'fatol': self.tolerance},
callback=self.callback)
Logger().get(LogLevel.info) << \
"DF-SANE/Scipy: {} ({} iterations, {})".format(
solution.message,
solution.nit,
self.tolerance)
if not solution.success:
raise NLNoConvergence("DF-SANE/Scipy did not converge")
return solution.x.copy()
def ToleranceManager(start, end, rate):
"""Decorate solver to manage tolerance of non-linear solve step."""
def actual_decorator(cls):
orig_init = cls.__init__
orig_solve = cls.solve
orig_update_state = cls.updateState
@wraps(cls.__init__)
def __init__(obj, *args, **kwargs):
orig_init(obj, *args, **kwargs)
obj.setToleranceManager(_tolerance_manager(start, end, rate))
@wraps(cls.solve)
def new_solve(obj, *args, **kwargs):
ftol = obj.tolerance
ftol *= rate
obj.tolerance = max(ftol, end)
return orig_solve(obj, *args, **kwargs)
@wraps(cls.updateState)
def updateState(obj, *args, **kwargs):
obj.tolerance = start
return orig_update_state(obj, *args, **kwargs)
cls.__init__ = __init__
# cls.solve = new_solve
# cls.updateState = updateState
return cls
return actual_decorator

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