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 = construct_weak_form(a, dim=DIM, is_block=True, verbose=True)
print('> weak form := {0}'.format(expr))
# ...
print('')
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_4a():
x, y, z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
b = Tuple(1.0, 0., 0.)
a = Lambda((x, y, z, v, u),
Dot(Curl(Cross(b, u)), Curl(Cross(b, v))) + 0.2 * Dot(u, v))
print('> input := {0}'.format(a))
# ...
expr = construct_weak_form(a, dim=DIM, is_block=True, verbose=True)
print('> weak 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 = construct_weak_form(a, dim=DIM, is_block=True)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_3d_4a():
x,y,z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
b = Tuple(1.0, 0., 0.)
a = Lambda((x,y,z,v,u), Dot(Curl(Cross(b,u)), Curl(Cross(b,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_scalar_4():
print('============== test_2d_scalar_4 ================')
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))
# ... create a finite element space
p1 = 2
p2 = 2
ne1 = 8
ne2 = 8
print('> Grid :: [{ne1},{ne2}]'.format(ne1=ne1, ne2=ne2))
print('> Degree :: [{p1},{p2}]'.format(p1=p1, p2=p2))
grid_1 = linspace(0., 1., ne1 + 1)
grid_2 = linspace(0., 1., ne2 + 1)
V1 = SplineSpace(p1, grid=grid_1)
V2 = SplineSpace(p2, grid=grid_2)
V = TensorFemSpace(V1, V2)
# ...
# ... create a glt symbol from a string without evaluation
expr = glt_symbol(a, space=V)
print('> glt symbol := {0}'.format(expr))
# ...
# ...
symbol_f90 = compile_symbol('symbol_scalar_4', a, V, backend='fortran')
# ...
# ... example of symbol evaluation
t1 = linspace(-pi, pi, ne1 + 1)
t2 = linspace(-pi, pi, ne2 + 1)
x1 = linspace(0., 1., ne1 + 1)
x2 = linspace(0., 1., ne2 + 1)
e = zeros((ne1 + 1, ne2 + 1), order='F')
symbol_f90(x1, x2, t1, t2, e)
# ...
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_block_4():
print('============== test_3d_block_4 ================')
"""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 = Constant('c0')
c1 = Constant('c1')
c2 = Constant('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))
# ... create a finite element space
p1 = 2
p2 = 2
p3 = 2
ne1 = 2
ne2 = 2
ne3 = 2
# ...
print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3))
print('> Degree :: [{},{},{}]'.format(p1, p2, p3))
grid_1 = linspace(0., 1., ne1 + 1)
grid_2 = linspace(0., 1., ne2 + 1)
grid_3 = linspace(0., 1., ne3 + 1)
V1 = SplineSpace(p1, grid=grid_1)
V2 = SplineSpace(p2, grid=grid_2)
V3 = SplineSpace(p3, grid=grid_3)
Vx = TensorFemSpace(V1, V2, V3)
Vy = TensorFemSpace(V1, V2, V3)
Vz = TensorFemSpace(V1, V2, V3)
V = VectorFemSpace(Vx, Vy, Vz)
# ...
# ... create a glt symbol from a string without evaluation
expr = glt_symbol(a, space=V)
print('> glt symbol := {0}'.format(expr))
# ...
# ...
symbol_f90 = compile_symbol('symbol_block_4',
a,
V,
d_constants={
'bx': 0.1,
'by': 1.,
'bz': 0.2,
'c0': 0.1,
'c1': 1.,
'c2': 1.
},
backend='fortran')
# ...
# ... example of symbol evaluation
t1 = linspace(-pi, pi, ne1 + 1)
t2 = linspace(-pi, pi, ne2 + 1)
t3 = linspace(-pi, pi, ne3 + 1)
x1 = linspace(0., 1., ne1 + 1)
x2 = linspace(0., 1., ne2 + 1)
x3 = linspace(0., 1., ne3 + 1)
e = zeros((3, 3, ne1 + 1, ne2 + 1, ne3 + 1), order='F')
symbol_f90(x1, x2, x3, t1, t2, t3, e)
# ...
print('')
def test_3d_block_3():
print('============== test_3d_block_3 ================')
x, y, z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
b = Tuple(1.0, 0., 0.)
a = Lambda((x, y, z, v, u),
Dot(Curl(Cross(b, u)), Curl(Cross(b, v))) + 0.2 * Dot(u, v))
print('> input := {0}'.format(a))
# ... create a finite element space
p1 = 2
p2 = 2
p3 = 2
ne1 = 2
ne2 = 2
ne3 = 2
# ...
print('> Grid :: [{},{},{}]'.format(ne1, ne2, ne3))
print('> Degree :: [{},{},{}]'.format(p1, p2, p3))
grid_1 = linspace(0., 1., ne1 + 1)
grid_2 = linspace(0., 1., ne2 + 1)
grid_3 = linspace(0., 1., ne3 + 1)
V1 = SplineSpace(p1, grid=grid_1)
V2 = SplineSpace(p2, grid=grid_2)
V3 = SplineSpace(p3, grid=grid_3)
Vx = TensorFemSpace(V1, V2, V3)
Vy = TensorFemSpace(V1, V2, V3)
Vz = TensorFemSpace(V1, V2, V3)
V = VectorFemSpace(Vx, Vy, Vz)
# ...
# ... create a glt symbol from a string without evaluation
expr = glt_symbol(a, space=V)
print('> glt symbol := {0}'.format(expr))
# ...
# ...
symbol_f90 = compile_symbol('symbol_block_3', a, V, backend='fortran')
# ...
# ... example of symbol evaluation
t1 = linspace(-pi, pi, ne1 + 1)
t2 = linspace(-pi, pi, ne2 + 1)
t3 = linspace(-pi, pi, ne3 + 1)
x1 = linspace(0., 1., ne1 + 1)
x2 = linspace(0., 1., ne2 + 1)
x3 = linspace(0., 1., ne3 + 1)
e = zeros((3, 3, ne1 + 1, ne2 + 1, ne3 + 1), order='F')
symbol_f90(x1, x2, x3, t1, t2, t3, e)
# ...
print('')