def test_linear_expr_2d_1():
domain = Domain('Omega', dim=2)
x, y = domain.coordinates
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
V = ScalarFunctionSpace('V', domain)
u, u1, u2 = [element_of(V, name=i) for i in ['u', 'u1', 'u2']]
v, v1, v2 = [element_of(V, name=i) for i in ['v', 'v1', 'v2']]
# ...
l = LinearExpr(v, x * y * v)
print(l)
print(l.expr)
print(l(v1))
# TODO
# print(l(v1+v2))
print('')
# ...
# ...
l = LinearExpr((v1, v2), x * v1 + y * v2)
print(l)
print(l.expr)
print(l(u1, u2))
# TODO
# print(l(u1+v1, u2+v2))
print('')
def test_linear_expr_2d_2():
domain = Domain('Omega', dim=2)
x, y = domain.coordinates
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
V = VectorFunctionSpace('V', domain)
u, u1, u2 = [element_of(V, name=i) for i in ['u', 'u1', 'u2']]
v, v1, v2 = [element_of(V, name=i) for i in ['v', 'v1', 'v2']]
g = Tuple(x, y)
l = LinearExpr(v, dot(g, v))
print(l)
print(l.expr)
print(l(v1))
# TODO
# print(l(v1+v2))
print('')
# ...
# ...
g1 = Tuple(x, 0)
g2 = Tuple(0, y)
l = LinearExpr((v1, v2), dot(g1, v1) + dot(g2, v2))
print(l)
print(l.expr)
print(l(u1, u2))
# TODO
# print(l(u1+v1, u2+v2))
print('')
def test_linearize_expr_2d_1():
domain = Domain('Omega', dim=2)
x,y = domain.coordinates
V1 = ScalarFunctionSpace('V1', domain)
W1 = VectorFunctionSpace('W1', domain)
v1 = element_of(V1, name='v1')
w1 = element_of(W1, name='w1')
alpha = Constant('alpha')
F = element_of(V1, name='F')
G = element_of(W1, 'G')
# ...
l = LinearExpr(v1, F**2*v1)
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(v1, dot(grad(F), grad(F))*v1)
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(v1, exp(-F)*v1)
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(v1, cos(F)*v1)
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(v1, cos(F**2)*v1)
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(v1, F**2*dot(grad(F), grad(v1)))
a = linearize(l, F, trials='u1')
print(a)
# ...
# ...
l = LinearExpr(w1, dot(rot(G), grad(G))*w1)
a = linearize(l, G, trials='u1')
print(a)
def test_linearize_expr_2d_2():
domain = Domain('Omega', dim=2)
x, y = domain.coordinates
V1 = ScalarFunctionSpace('V1', domain)
v1 = element_of(V1, name='v1')
alpha = Constant('alpha')
F = element_of(V1, name='F')
G = element_of(V1, name='G')
# ...
l1 = LinearExpr(v1, F**2 * v1)
l = LinearExpr(v1, l1(v1))
a = linearize(l, F, trials='u1')
print(a)
expected = linearize(l1, F, trials='u1')
assert (linearize(l, F, trials='u1') == expected)