def assemble_F(self, Y=None):
if Y is None:
Y = zeros((self._ndofs,))
F = zeros((self._ndofs,))
for m in self._meshes:
for el_num, e in enumerate(m.elements):
for i in range(len(e.dofs)):
i_glob = e.dofs[i]
if i_glob == -1:
continue
mi = self.get_mesh_number(i_glob)
def func1(x):
# x is the integration point, we need to determine
# the values of y1, y2, ... at this integration
# point.
v = 0.
for j in range(len(e.dofs)):
g = e.dofs[j]
if g == -1:
coeff = e.get_dirichlet_value(j)
#print "XX", e.dofs, j
else:
coeff = Y[g]
v += coeff*e.shape_function_deriv(j, x)
#print "deriv", el_num, x, v
v = v*e.shape_function(i, x)
return v
du_phi, err = quadrature(func1, -1, 1)
def func2(x):
# x is the integration point, we need to determine
# the values of y1, y2, ... at this integration
# point.
# XXX: this only works if all the meshes are the same:
y = [self.get_sol_value(_i, el_num, Y, x) for _i \
in range(len(self._meshes))]
x_phys = e.ref2phys(x)
return self._F(mi, y, x_phys) * e.shape_function(i, x)
#if el_num == 0:
# print "func", func2(array([-1, -0.9, -0.5, 0, 0.5, 0.9,
# 1]))
#print "f", f(0, array([-1, -0.9, -0.5, 0, 0.5, 0.9,
# 1]))
#print "func", func2(array([-1, -0.9, -0.5, 0, 0.5, 0.9,
# 1]))
#stop
f_phi, err = quadrature(func2, -1., 1.)
f_phi *= e.jacobian
#print "X", i_glob, el_num, i, du_phi, f_phi
F[i_glob] += du_phi - f_phi
#print Y
#print "get_sol_value"
#print self.get_sol_value(0, 0, Y, 1)
return F
def integrate_dphi_phi(self, i, j):
"""
Calculates the integral of dphi*phi on the reference element
"""
def func(x):
return self.shape_function_deriv(i, x) * self.shape_function(j, x)
i, err = quadrature(func, -1, 1)
return i
def assemble_J(self, Y):
J = zeros((self._ndofs, self._ndofs))
for m in self._meshes:
for e in m.elements:
for i in range(len(e.dofs)):
for j in range(len(e.dofs)):
i_glob = e.dofs[i]
j_glob = e.dofs[j]
if i_glob == -1 or j_glob == -1:
continue
mi = self.get_mesh_number(i_glob)
mj = self.get_mesh_number(j_glob)
def func(x):
# x is the integration point, we need to determine
# the values of y1, y2, ... at this integration
# point.
# XXX: This only works for linear problems (it
# doesn't matter what those values are), but it's
# wrong for nonlinear ones and it needs to be
# fixed:
nmeshes = len(self._meshes)
W = [0]*nmeshes
x_phys = e.ref2phys(x)
f_user = self._DFDY(mi, mj, W, x_phys)
return f_user * \
e.shape_function(i, x) * \
e.shape_function(j, x)
dphi_phi = e.integrate_dphi_phi(j, i)
df_phi_phi, err = quadrature(func, -1, 1)
df_phi_phi *= e.jacobian
J[i_glob, j_glob] += dphi_phi - df_phi_phi
#print f(0, array([-1, -0.9, 0, 0.7, 0.9, 1]))
#stop
#print "X", i_glob, j_glob, i, dphi_phi, df_phi_phi
return J