def test_mesh9():
n1 = Node(1)
n2 = Node(3)
n3 = Node(4)
n4 = Node(5)
e1 = Element(n1, n2, order=3)
e2 = Element(n2, n3, order=1)
e3 = Element(n3, n4, order=2)
nodes = (n1, n2, n3, n4)
elements = (e1, e2, e3)
m1 = Mesh(nodes, elements)
m1.set_bc(left=False, value=1)
e4 = Element(n1, n2, order=3)
e5 = Element(n2, n3, order=1)
e6 = Element(n3, n4, order=2)
elements = (e4, e5, e6)
m2 = Mesh(nodes, elements)
m2.set_bc(left=True, value=1)
d = DiscreteProblem(meshes=[m1, m2])
ndofs = d.assign_dofs()
assert m1.elements[0].dofs[0] == 0
assert m1.elements[0].dofs[1] == 1
assert m1.elements[0].dofs[2] == 3
assert m1.elements[0].dofs[3] == 4
assert m1.elements[1].dofs[0] == 1
assert m1.elements[1].dofs[1] == 2
assert m1.elements[2].dofs[0] == 2
assert m1.elements[2].dofs[1] == -1
assert m1.elements[2].dofs[2] == 5
assert m2.elements[0].dofs[0] == -1
assert m2.elements[0].dofs[1] == 0 + 6
assert m2.elements[0].dofs[2] == 3 + 6
assert m2.elements[0].dofs[3] == 4 + 6
assert m2.elements[1].dofs[0] == 0 + 6
assert m2.elements[1].dofs[1] == 1 + 6
assert m2.elements[2].dofs[0] == 1 + 6
assert m2.elements[2].dofs[1] == 2 + 6
assert m2.elements[2].dofs[2] == 5 + 6
assert ndofs == 12
assert d.get_mesh_number(0) == 0
assert d.get_mesh_number(4) == 0
assert d.get_mesh_number(5) == 0
assert d.get_mesh_number(6) == 1
assert d.get_mesh_number(11) == 1
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)
"""
from hermes1d import Node, Element, Mesh, DiscreteProblem
from numpy import zeros
a = 0.
b = 1.
N = 10
nodes = [Node((b-a)/N * i) for i in range(N)]
elements = [Element(nodes[i], nodes[i+1], order=1) for i in range(N-1)]
m1 = Mesh(nodes, elements)
m1.set_bc(left=True, value=1)
elements = [Element(nodes[i], nodes[i+1], order=1) for i in range(N-1)]
m2 = Mesh(nodes, elements)
m2.set_bc(left=True, value=2)
d = DiscreteProblem(meshes=[m1, m2])
k = 1.0
def F(i, Y, t):
if i == 0:
return -Y[0]+Y[1]
elif i == 1:
return Y[1]
raise ValueError("Wrong i (i=%d)." % (i))
def DFDY(i, j, Y, t):
if i == 0 and j == 0:
return -1
elif i == 0 and j == 1:
return 1
elif i == 1 and j == 0:
return 0
elif i == 1 and j == 1:
# define nodes:
nodes = [Node(x) for x in x_values]
# define elements of the 1st mesh
elements = [Element(nodes[i], nodes[i+1], order=2) for i in range(N)]
m1 = Mesh(nodes, elements)
m1.set_bc(left=True, value=0)
# define elements of the 2nd mesh
elements = [Element(nodes[i], nodes[i+1], order=1) for i in range(N)]
m2 = Mesh(nodes, elements)
m2.set_bc(left=True, value=1)
# definition of the ODE system:
d = DiscreteProblem(meshes=[m1, m2])
# definition of the RHS:
def F(i, Y, t):
if i == 0:
return Y[1]
elif i == 1:
return -Y[0]
raise ValueError("Wrong i (i=%d)." % (i))
# definition of the Jacobian matrix
def DFDY(i, j, Y, t):
if i == 0 and j == 0:
return 0.
elif i == 0 and j == 1:
return 1.
