def test_3d_4b():
"""Alfven operator."""
x,y,z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
bx = Constant('bx')
by = Constant('by')
bz = Constant('bz')
b = Tuple(bx, by, bz)
c0,c1,c2 = symbols('c0 c1 c2')
a = Lambda((x,y,z,v,u), ( c0 * Dot(u, v)
- c1 * Div(u) * Div(v)
+ c2 *Dot(Curl(Cross(b,u)), Curl(Cross(b,v)))))
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr, info = initialize_weak_form(expr, dim=DIM)
print('> temp form :=')
# for a nice printing, we print the dictionary entries one by one
for key, value in list(expr.items()):
print('\t\t', key, '\t', value)
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')
def test_3d_1():
x,y,z = symbols('x y z')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x,y,z,v,u), Dot(Grad(u), Grad(v)))
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr, info = initialize_weak_form(expr, dim=DIM)
print('> temp form := {0}'.format(expr))
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')
def test_2d_3():
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, y, v, u), Cross(Curl(u), Curl(v)) + 0.2 * u * v)
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr, info = initialize_weak_form(expr, dim=DIM)
print('> temp form := {0}'.format(expr))
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')
def test_3d_3():
x,y,z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
a = Lambda((x,y,z,v,u), Dot(Curl(u), Curl(v)) + 0.2 * Dot(u, v))
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr, info = initialize_weak_form(expr, dim=DIM)
print('> temp form :=')
# for a nice printing, we print the dictionary entries one by one
for key, value in list(expr.items()):
print('\t\t', key, '\t', value)
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')
def test_2d_4():
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
bx = Constant('bx')
by = Constant('by')
b = Tuple(bx, by)
a = Lambda((x, y, v, u), 0.2 * u * v + Dot(b, Grad(v)) * u)
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr, info = initialize_weak_form(expr, dim=DIM)
print('> temp form := {0}'.format(expr))
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')