def test_funspace_2():
'''Test of FunctionSpace.int_phi_phi made up of linear elements, basic
integration
'''
ox, dx, nx = 0., 1., 1
mesh = Mesh(type='uniform', lx=dx, nx=nx, block='B1')
V = FunctionSpace(mesh, {'B1': Element(type='link2')})
# basic properties
assert V.num_dof == (nx + 1)
assert V.size == nx
X = np.linspace(ox, dx, nx+1)
assert allclose(V.X, X)
# Integrate[N(x) N(x) {x, 0, 1}]
fun = lambda x: x
f = lambda i, j: integrate(fun(x) * N[i] * N[j], (x, ox, dx))
ans = V.int_phi_phi(fun=fun, derivative=(False, False))
exact = Matrix(2, 2, lambda i, j: f(i,j))
assert areclose(exact, ans)
# Trivial check with coefficient
fun = lambda x: 1.
a1 = V.int_phi_phi()
a2 = V.int_phi_phi(fun=fun)
assert areclose(a1, a2)
def test_solve_system():
from numerix import areclose, allclose
sys.stdout.write('testing solve_system... ')
sys.stdout.flush()
n = 1000
offset = 0
xa, xb = 0., 1.
nodes, vertices, elements, connect = simplemesh(xa, xb, n)
A, E, P = 1., 100., 10.
k = np.zeros(n)
for (el, econn) in enumerate(connect):
i, j = nodes.index(econn[0]), nodes.index(econn[1])
k[el] = A * E / (vertices[j] - vertices[i])
delta = .05
bcs = [(nodes[0],'x', delta)]
cfs = [(nodes[-1], 'x', P)]
u, r = solve_system(nodes, vertices, elements, connect, k, bcs, cfs)
# check the error
K = A * E / (xb - xa)
d = P / K + delta
assert areclose(d, u[-1])
assert areclose(P, -r[0])
assert allclose(r[1:], 0.)
sys.stdout.write('success\n')
def test_solve_system():
from numerix import areclose, allclose
sys.stdout.write('testing solve_system... ')
sys.stdout.flush()
n = 1000
offset = 0
xa, xb = 0., 1.
nodes, vertices, elements, connect = simplemesh(xa, xb, n)
A, E, P = 1., 100., 10.
k = np.zeros(n)
for (el, econn) in enumerate(connect):
i, j = nodes.index(econn[0]), nodes.index(econn[1])
k[el] = A * E / (vertices[j] - vertices[i])
delta = .05
bcs = [(nodes[0], 'x', delta)]
cfs = [(nodes[-1], 'x', P)]
u, r = solve_system(nodes, vertices, elements, connect, k, bcs, cfs)
# check the error
K = A * E / (xb - xa)
d = P / K + delta
assert areclose(d, u[-1])
assert areclose(P, -r[0])
assert allclose(r[1:], 0.)
sys.stdout.write('success\n')
def test_funspace_1():
'''Test of FunctionSpace.int_phi made up of linear elements'''
ox, dx, nx = 0., 10., 5
mesh = Mesh(type='uniform', lx=dx, nx=nx, block='B1')
V = FunctionSpace(mesh, {'B1': Element(type='link2')})
# basic properties
assert V.num_dof == (nx + 1)
assert V.size == nx
X = np.linspace(ox, dx, nx+1)
assert allclose(V.X, X)
# Integrate[1, {x, ox, lx}]
f = lambda x: 1
ans = np.sum(V.int_phi(f))
exact = V.X[-1]
assert areclose(ans, exact)
# Integrate[x, {x, ox, lx}]
f = lambda x: x
ans = np.sum(V.int_phi(f))
exact = V.X[-1] ** 2 / 2.
assert areclose(ans, exact)
# Integrate[x**2, {x, ox, lx}]
f = lambda x: x * x
ans = np.sum(V.int_phi(f))
exact = V.X[-1] ** 3 / 3.
assert areclose(ans, exact)
# Integrate[x**3, {x, ox, lx}]
f = lambda x: x * x * x
ans = np.sum(V.int_phi(f))
exact = V.X[-1] ** 4 / 4.
assert areclose(ans, exact)
# Integrate[x**4, {x, ox, lx}]
f = lambda x: x * x * x * x
ans = np.sum(V.int_phi(f))
exact = V.X[-1] ** 5 / 5.
assert areclose(ans, exact, tol=1.5)
def test_funspace_8():
'''Testing of FunctionSpace.int_phi_phi, MMS'''
ox, dx, nx = 0., 10., 10
mesh = Mesh(type='uniform', lx=dx, nx=nx, block='B1')
V = FunctionSpace(mesh, {'B1': Element(type='link2')})
rhs = np.random.rand(V.num_dof)
A = V.int_phi_phi()
f = lambda x: np.interp(x, V.X, rhs)
b = V.int_phi(f)
assert areclose(np.dot(A, rhs), b)
return
def test_funspace_7():
'''Test of FunctionSpace.int_phi_phi made up of linear elements, mixed
matrix integration
'''
ox, dx, nx = 0., 1., 1
mesh = Mesh(type='uniform', lx=dx, nx=nx, block='B1')
V = FunctionSpace(mesh, {'B1': Element(type='link2')})
# Integrate[N(x) N'(x) {x, 0, 1}]
f = lambda i, j: integrate(N[i] * dN[j], (x, ox, dx))
ans = V.int_phi_phi(derivative=(False, True))
exact = Matrix(2, 2, lambda i, j: f(i,j))
assert areclose(exact, ans)
# Integrate[N'(x) N(x) {x, 0, 1}]
f = lambda i, j: integrate(dN[i] * N[j], (x, ox, dx))
ans = V.int_phi_phi(derivative=(True, False))
exact = Matrix(2, 2, lambda i, j: f(i,j))
assert areclose(exact, ans)
return
def test_solve_system():
'''Test simple ifem solver'''
n = 1000
offset = 0
xa, xb = 0., 1.
nodes, vertices, elements, connect = simplemesh(xa, xb, n)
A, E, P = 1., 100., 10.
k = np.zeros(n)
for (el, econn) in enumerate(connect):
i, j = nodes.index(econn[0]), nodes.index(econn[1])
k[el] = A * E / (vertices[j] - vertices[i])
delta = .05
bcs = [(nodes[0],'x', delta)]
cfs = [(nodes[-1], 'x', P)]
u, r = solve_system(nodes, vertices, elements, connect, k, bcs, cfs)
# check the error
K = A * E / (xb - xa)
d = P / K + delta
assert areclose(d, u[-1])
assert areclose(P, -r[0])
assert allclose(r[1:], 0.)
def test_linear_element():
'''Test the implementation of the linear element with simple integrals'''
dx = 5.
num_elem = 5
mesh = Mesh(type='uniform', ox=0., lx=dx, nx=num_elem)
elem_num = 1
connect = mesh.connectivity(elem_num)
vertices = mesh.coordinates(connect)
elem = LinearElement(elem_num, connect, vertices)
# --- test some integrals
ex = lambda x: x
ex2 = lambda x: x ** 2
# Integrate[phi]
ans = elem.integrate()
exact = integrate(N, (x, 0, 1))
assert areclose(ans, exact)
# Integrate[dphi]
ans = elem.integrate(derivative=True)
exact = integrate(dN, (x, 0, 1))
assert areclose(ans, exact)
# Integrate[x phi]
ans = elem.integrate(ex)
exact = integrate(x * N, (x, 0, 1))
assert areclose(ans, exact)
# Integrate[x dphi]
ans = elem.integrate(ex, derivative=True)
exact = integrate(x * dN, (x, 0, 1))
assert areclose(ans, exact)
# Integrate[x x phi]
ans = elem.integrate(ex, ex)
exact = integrate(x * x * N, (x, 0, 1))
assert areclose(ans, exact)
# Integrate[x x dphi]
ans = elem.integrate(ex,ex,derivative=True)
exact = integrate(x*x*dN,(x,0,1))
assert areclose(ans, exact)