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dynamic_solver.py
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Wed, May 29, 02:00

dynamic_solver.py
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# ------------------------------------------------------------------------------
__author__ = "Nicolas Richart"
__copyright__ = "Copyright (C) 2016-2018, EPFL (Ecole Polytechnique Fédérale" \
" de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
" en Mécanique des Solides)"
__credits__ = ["Nicolas Richart"]
__license__ = "L-GPLv3"
__maintainer__ = "Nicolas Richart"
__email__ = "nicolas.richart@epfl.ch"
# ------------------------------------------------------------------------------
import copy
import numpy.linalg as npl
import scipy.sparse as sp
import scipy.sparse.linalg as spl
from . import export
from . import fe
@export
class DynamicSolver(fe.Solver):
def __init__(self, model, **kwargs):
opt = copy.copy(kwargs)
self._delta_t = opt.pop("delta_t", 0.001)
self._alpha = opt.pop("alpha", 1./2.)
self._beta = opt.pop("beta", 1./2.)
self._type = opt.pop("type", 'disp')
self._tolerance = opt.pop("tolerance", 1e-10)
self._max_nloops = opt.pop("max_iterations", 100)
self._model = model
self._J = sp.csr_matrix(self._model.K.shape)
self._coeff = {'disp': {'disp': 1.,
'velo': 1. / (self._alpha * self._delta_t),
'acce': 1. / (self._alpha * self._beta * self._delta_t ** 2)}, # NOQA: E501
'velo': {'disp': self._alpha * self._delta_t,
'velo': 1.,
'acce': 1. / (self._beta * self._delta_t)},
'acce': {'disp': self._alpha * self._beta * self._delta_t ** 2, # NOQA: E501
'velo': self._beta * self._delta_t,
'acce': 1.}}
def _assembleResidual(self):
self._r = self._model.f_ext - self._model.f_int - \
self._model.M * self._model.a
C = self._model.C
if C is not None:
self._r -= C * self._model.v
def _predictor(self):
self._model.u += self._delta_t * self._model.v + \
self._delta_t ** 2 / 2. * self._model.a
self._model.v += self._delta_t * self._model.a
def _corrector(self, delta_):
self._model.u += self._coeff[self._type]['disp'] * delta_
self._model.v += self._coeff[self._type]['velo'] * delta_
self._model.a += self._coeff[self._type]['acce'] * delta_
def _assembleJacobian(self):
K = self._model.K
e = self._coeff[self._type]['disp']
self._J = e * K
C = self._model.C
if C is not None:
d = self._coeff[self._type]['velo']
self._J += d * C
M = self._model.M
if M is not None:
c = self._coeff[self._type]['acce']
self._J += c * M
self._model.applyDirichletBC()
self._zero_rows(self._J, self._model.blocked)
def solveStep(self):
self._predictor()
self._nloops = 0
converged = False
while not converged:
self._assembleJacobian()
self._assembleResidual()
delta_ = spl.spsolve(self._J, self._r)
self._corrector(delta_)
self._nloops += 1
error = npl.norm(delta_)
converged = error < self._tolerance or \
self._nloops > self._max_nloops
print("{0} {1} -> {2}".format(error, self._nloops, converged))
if self._nloops >= self._max_nloops:
raise ValueError('The solver did not converge')
@property
def nloops(self):
return self._nloops

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