def test_3d_block_2():
print('============== test_3d_block_2 ================')
x, y, z = symbols('x y z')
u = IndexedBase('u')
v = IndexedBase('v')
F = Field('F')
a = Lambda((x, y, z, v, u),
Dot(Curl(u), Curl(v)) + 0.2 * Dot(u, v) + F * u[0] * v[0])
# ... 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)
W = TensorFemSpace(V1, V2, V3)
# ...
# ... vector space
V = VectorFemSpace(W, W, W)
# ...
F = Spline(W)
F.coeffs._data[:, :, :] = 1.
# ...
kernel_py = compile_kernel('kernel_block_2', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_block_2', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py, fields={'F': F})
M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F})
# ...
assert_identical_coo(M_py, M_f90)
def test_2d_block_2():
print('============== test_2d_block_2 ================')
# ... define the weak formulation
x, y = symbols('x y')
u = IndexedBase('u')
v = IndexedBase('v')
F = Field('F')
a = Lambda(
(x, y, v, u),
Rot(u) * Rot(v) + Div(u) * Div(v) + 0.2 * Dot(u, v) + F * u[0] * v[0])
# ...
# ... 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)
W = TensorFemSpace(V1, V2)
# ...
# ... vector space
V = VectorFemSpace(W, W)
# ...
F = Spline(W)
F.coeffs._data[:, :] = 1.
# ...
kernel_py = compile_kernel('kernel_block_2', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_block_2', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py, fields={'F': F})
M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F})
# ...
assert_identical_coo(M_py, M_f90)
def test_3d_scalar_4():
print('============== test_3d_scalar_4 ================')
# ... define the weak formulation
x, y, z = symbols('x y z')
u = Symbol('u')
v = Symbol('v')
F = Field('F')
a = Lambda((x, y, z, v, u), Dot(Grad(F * u), Grad(v)) + u * v)
# ...
# ... 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)
V = TensorFemSpace(V1, V2, V3)
# ...
F = Spline(V)
F.coeffs._data[:, :, :] = 1.
# ...
kernel_py = compile_kernel('kernel_scalar_4', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_scalar_4', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py, fields={'F': F})
M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F})
# ...
assert_identical_coo(M_py, M_f90)
def test_1d_4():
x,y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
F = Field('F')
a = Lambda((x,y,v,u), Dot(Grad(F*u), Grad(v)) + u*v)
print('> input := {0}'.format(a))
expr = gelatize(a, dim=DIM)
print('> gelatized := {0}'.format(expr))
expr = normalize_weak_from(expr)
print('> normal form := {0}'.format(expr))
print('')
def test_1d_scalar_4():
print('============== test_1d_scalar_4 ================')
# ... define the weak formulation
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
F = Field('F')
a = Lambda((x, v, u), Dot(Grad(F * u), Grad(v)) + u * v)
# ...
# ... create a finite element space
p = 3
ne = 64
print('> Grid :: {ne}'.format(ne=ne))
print('> Degree :: {p}'.format(p=p))
grid = linspace(0., 1., ne + 1)
V = SplineSpace(p, grid=grid)
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_4', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_scalar_4', a, V, backend='fortran')
F = Spline(V)
F.coeffs._data[:] = 1.
M_py = assemble_matrix(V, kernel_py, fields={'F': F})
M_f90 = assemble_matrix(V, kernel_f90, fields={'F': F})
# ...
assert_identical_coo(M_py, M_f90)