def test_discrete_problem2():
n1 = Node(0)
n2 = Node(1)
n3 = Node(2)
n4 = Node(3)
e1 = Element(n1, n2, order=1)
e2 = Element(n2, n3, order=1)
e3 = Element(n3, n4, order=1)
nodes = (n1, n2, n3, n4)
elements = (e1, e2, e3)
m1 = Mesh(nodes, elements)
m1.set_bc(left=True, value=1)
d = DiscreteProblem(meshes=[m1])
def F(i, Y, t):
if i == 0:
return -Y[0]
raise ValueError("Wrong i (i=%d)." % (i))
def DFDY(i, j, Y, t):
if i == 0 and j == 0:
return -1
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
d.define_ode(F, DFDY)
d.assign_dofs()
Y = zeros((d.ndofs,))
J = d.assemble_J(Y)
F = d.assemble_F()
x = d.solve(J, F)
def _test_discrete_problem1():
n1 = Node(0)
n2 = Node(1)
n3 = Node(2)
n4 = Node(3)
e1 = Element(n1, n2, order=1)
e2 = Element(n2, n3, order=1)
e3 = Element(n3, n4, order=1)
nodes = (n1, n2, n3, n4)
elements = (e1, e2, e3)
m1 = Mesh(nodes, elements)
m1.set_bc(left=True, value=0)
e4 = Element(n1, n2, order=1)
e5 = Element(n2, n3, order=1)
e6 = Element(n3, n4, order=1)
elements = (e4, e5, e6)
m2 = Mesh(nodes, elements)
m2.set_bc(left=True, value=1)
d = DiscreteProblem(meshes=[m1, m2])
def F(i, Y, t):
if i == 0:
return Y[1]
elif i == 1:
k = 2.0
return -k**2 * Y[0]
raise ValueError("Wrong i (i=%d)." % (i))
def DFDY(i, j, Y, t):
k = 2.0
if i == 0 and j == 0:
return 0.
elif i == 0 and j == 1:
return 1.
elif i == 1 and j == 0:
return -k**2
elif i == 1 and j == 1:
return 0.
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
d.set_rhs(F, DFDY)
d.assign_dofs()
J = d.assemble_J()
F = d.assemble_F()
x = d.solve(J, F)
return -1
elif i == 0 and j == 1:
return 1
elif i == 1 and j == 0:
return 0
elif i == 1 and j == 1:
return 1
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
d.define_ode(F, DFDY)
d.assign_dofs()
Y = zeros(d.ndofs)
J = d.assemble_J(Y)
error = 1e10
i = 0
while error > 1e-10:
F = d.assemble_F(Y)
dY = d.solve(J, F)
error = d.calculate_error_l2_norm(dY)
print "it=%d, l2_norm=%e" % (i, error)
Y += dY
i += 1
x = Y
from pylab import plot, legend, show
sln1, sln2 = d.linearize(x, 5)
x1, y1 = sln1
x2, y2 = sln2
plot(x1, y1, label="$u_1$")
plot(x2, y2, label="$u_2$")
legend()
show()
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
# assign both F and J to the discrete problem:
d.define_ode(F, DFDY)
# enumeration of unknowns:
d.assign_dofs()
# definition of the initial condition for the global Newton method:
Y = d.get_initial_condition_euler()
#plot_Y(Y, a, b)
#stop
#Y = zeros((d.ndofs,))
# Newton's iteration:
error = 1e10
i = 0
J = d.assemble_J(Y)
while error > 1e-5:
F = d.assemble_F(Y)
dY = d.solve(J, F)
Y += dY
#plot_Y(Y, a, b)
error_dY = d.calculate_error_l2_norm(dY)
error_F = d.calculate_error_l2_norm(d.assemble_F(Y))
print "it=%d, l2_norm_dY=%e, l2_norm_F=%e" % (i, error_dY, error_F)
error = max(error_dY, error_F)
i += 1
plot_Y(Y, a, b)
