def get_A_GaNi(self, N, primaldual='primal'):
"""
Returns stiffness matrix for a scheme with trapezoidal quadrature rule.
"""
coord = Grid.get_coordinates(N, self.Y)
A = self.evaluate(coord)
if primaldual is 'dual':
A = A.inv()
return A
def get_A_GaNi(self, N, primaldual='primal'):
"""
Returns stiffness matrix for a scheme with trapezoidal quadrature rule.
"""
coord = Grid.get_coordinates(N, self.Y)
A = self.evaluate(coord)
if primaldual is 'dual':
A = A.inv()
return A
def get_A_Ga(self, Nbar, primaldual='primal', order=None, P=None):
""" Returns stiffness matrix for scheme with exact integration."""
if order is None and 'order' in self.conf:
order = self.conf['order']
if order is None:
shape_funs = self.get_shape_functions(Nbar)
val = np.zeros(self.conf['vals'][0].shape + shape_funs[0].shape)
for ii in range(len(self.conf['inclusions'])):
if primaldual is 'primal':
Aincl = self.conf['vals'][ii]
elif primaldual is 'dual':
Aincl = np.linalg.inv(self.conf['vals'][ii])
val += np.einsum('ij...,k...->ijk...', Aincl, shape_funs[ii])
return Matrix(name='A_Ga', val=val, Fourier=False)
else:
if P is None and 'P' in self.conf:
P = self.conf['P']
coord = Grid.get_coordinates(P, self.Y)
vals = self.evaluate(coord)
dim = vals.d
if primaldual is 'dual':
vals = vals.inv()
h = self.Y/P
if order in [0, 'constant']:
Wraw = get_weights_con(h, Nbar, self.Y)
elif order in [1, 'bilinear']:
Wraw = get_weights_lin(h, Nbar, self.Y)
Aapp = np.zeros(np.hstack([dim, dim, Nbar]))
for m in np.arange(dim):
for n in np.arange(dim):
hAM0 = DFT.fftnc(vals[m, n], P)
if np.allclose(P, Nbar):
hAM = hAM0
elif np.all(np.greater_equal(P, Nbar)):
hAM = decrease(hAM0, Nbar)
elif np.all(np.less(P, Nbar)):
factor = np.ceil(np.array(Nbar, dtype=np.float64) / P)
hAM0per = np.tile(hAM0, 2*factor-1)
hAM = decrease(hAM0per, Nbar)
else:
raise ValueError()
pNbar = np.prod(Nbar)
""" if DFT is normalized in accordance with articles there
should be np.prod(M) instead of np.prod(Nbar)"""
Aapp[m, n] = np.real(pNbar*DFT.ifftnc(Wraw*hAM, Nbar))
name = 'A_Ga_o%d_P%d' % (order, P.max())
return Matrix(name=name, val=Aapp, Fourier=False)
def savefig(self, fname='material.pdf', N=50*np.ones(2)):
import pylab as pl
pl.figure(num=None, figsize=(3,3), dpi=1000)
coord = Grid.get_coordinates(N, self.Y)
vals = self.evaluate(coord)[0, 0]
pl.pcolor(coord[0], coord[1], -vals)
pl.xlim([-self.Y[0]/2, self.Y[0]/2])
pl.ylim([-self.Y[1]/2, self.Y[1]/2])
pl.xlabel(r'coordinate $x_1$')
pl.ylabel(r'coordinate $x_2$')
pl.savefig(fname, pad_inches=0.02, bbox_inches='tight')
pl.close()
def savefig(self, fname='material.pdf', N=50 * np.ones(2)):
import pylab as pl
pl.figure(num=None, figsize=(3, 3), dpi=1000)
coord = Grid.get_coordinates(N, self.Y)
vals = self.evaluate(coord)[0, 0]
pl.pcolor(coord[0], coord[1], -vals)
pl.xlim([-self.Y[0] / 2, self.Y[0] / 2])
pl.ylim([-self.Y[1] / 2, self.Y[1] / 2])
pl.xlabel(r'coordinate $x_1$')
pl.ylabel(r'coordinate $x_2$')
pl.savefig(fname, pad_inches=0.02, bbox_inches='tight')
pl.close()
def get_A_Ga(self, Nbar, primaldual='primal', order=-1, P=None):
"""
Returns stiffness matrix for scheme with exact integration.
"""
if order == -1:
if 'order' in self.conf:
order = self.conf['order']
else:
raise ValueError('The material order is undefined!')
elif order not in [None, 'exact', 0, 1]:
raise ValueError('Wrong material order (%s)!' % str(order))
if order in [None, 'exact']:
shape_funs = self.get_shape_functions(Nbar)
val = np.zeros(self.conf['vals'][0].shape + shape_funs[0].shape)
for ii in range(len(self.conf['inclusions'])):
if primaldual is 'primal':
Aincl = self.conf['vals'][ii]
elif primaldual is 'dual':
Aincl = np.linalg.inv(self.conf['vals'][ii])
val += np.einsum('ij...,k...->ijk...', Aincl, shape_funs[ii])
name = 'A_Ga'
else:
if P is None and 'P' in self.conf:
P = self.conf['P']
coord = Grid.get_coordinates(P, self.Y)
vals = self.evaluate(coord)
dim = vals.d
if primaldual is 'dual':
vals = vals.inv()
h = self.Y / P
if order in [0, 'constant']:
Wraw = get_weights_con(h, Nbar, self.Y)
elif order in [1, 'bilinear']:
Wraw = get_weights_lin(h, Nbar, self.Y)
val = np.zeros(np.hstack([dim, dim, Nbar]))
for m in np.arange(dim):
for n in np.arange(dim):
hAM0 = DFT.fftnc(vals[m, n], P)
if np.allclose(P, Nbar):
hAM = hAM0
elif np.all(np.greater_equal(P, Nbar)):
hAM = decrease(hAM0, Nbar)
elif np.all(np.less(P, Nbar)):
factor = np.ceil(np.array(Nbar, dtype=np.float64) / P)
hAM0per = np.tile(hAM0, 2 * factor - 1)
hAM = decrease(hAM0per, Nbar)
else:
raise ValueError()
pNbar = np.prod(Nbar)
""" if DFT is normalized in accordance with articles there
should be np.prod(M) instead of np.prod(Nbar)"""
val[m, n] = np.real(pNbar * DFT.ifftnc(Wraw * hAM, Nbar))
name = 'A_Ga_o%d_P%d' % (order, P.max())
return Matrix(name=name, val=val, Fourier=False)
def get_A_GaNi(self, N, primaldual='primal'):
coord = Grid.get_coordinates(N, self.Y)
A = self.evaluate(coord)
if primaldual is 'dual':
A = A.inv()
return A
