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_block_2():
print('============== test_3d_block_2 ================')
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))
# ... 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_2', 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('')
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_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 = construct_weak_form(a, dim=DIM, is_block=True, verbose=True)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_1d_scalar_1():
print('============== test_1d_scalar_1 ================')
# ... define the weak formulation
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, v, u), Dot(Grad(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_1', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_scalar_1', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py)
M_f90 = assemble_matrix(V, kernel_f90)
# ...
assert_identical_coo(M_py, M_f90)
def test_2d_block_3():
print('============== test_2d_block_3 ================')
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
epsilon = Constant('epsilon')
Laplace = lambda v, u: Dot(Grad(v), Grad(u))
Mass = lambda v, u: v * u
u1, u2, p = symbols('u1 u2 p')
v1, v2, q = symbols('v1 v2 q')
a = Lambda((x, y, v1, v2, q, u1, u2, p),
Laplace(v1, u1) - dx(v1) * p + Laplace(v2, u2) - dy(v2) * p +
q * (dx(u1) + dy(u2)) + epsilon * Mass(q, p))
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)
V = VectorFemSpace(V, V, V)
# ...
# ...
kernel_py = compile_kernel('kernel_block_3',
a,
V,
d_args={'epsilon': 'double'},
backend='python')
kernel_f90 = compile_kernel('kernel_block_3',
a,
V,
d_args={'epsilon': 'double'},
backend='fortran')
M_py = assemble_matrix(V, kernel_py, args={'epsilon': 1.e-3})
M_f90 = assemble_matrix(V, kernel_f90, args={'epsilon': 1.e-3})
# ...
assert_identical_coo(M_py, M_f90)
print('')
def test_3d_scalar_2():
print('============== test_3d_scalar_2 ================')
# ... define the weak formulation
x, y, z = symbols('x y z')
u = Symbol('u')
v = Symbol('v')
alpha = Constant('alpha')
nu = Constant('nu')
a = Lambda((x, v, u), alpha * Dot(Grad(u), Grad(v)) + nu * 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)
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_2',
a,
V,
d_constants={'nu': 0.1},
d_args={'alpha': 'double'},
backend='python')
kernel_f90 = compile_kernel('kernel_scalar_2',
a,
V,
d_constants={'nu': 0.1},
d_args={'alpha': 'double'},
backend='fortran')
M_py = assemble_matrix(V, kernel_py, args={'alpha': 2.0})
M_f90 = assemble_matrix(V, kernel_f90, args={'alpha': 2.0})
# ...
assert_identical_coo(M_py, M_f90)
def test_2d_block_1():
print('============== test_2d_block_1 ================')
x, y = symbols('x y')
u = IndexedBase('u')
v = IndexedBase('v')
a = Lambda((x, y, v, u),
Rot(u) * Rot(v) + Div(u) * Div(v) + 0.2 * Dot(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)
Vx = TensorFemSpace(V1, V2)
Vy = TensorFemSpace(V1, V2)
V = VectorFemSpace(Vx, Vy)
# ...
# ... 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_2', 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((2, 2, ne1 + 1, ne2 + 1), order='F')
symbol_f90(x1, x2, t1, t2, e)
# ...
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_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_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 = construct_weak_form(a, dim=DIM)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_2d_2():
x, y = symbols('x y')
u = IndexedBase('u')
v = IndexedBase('v')
a = Lambda((x, y, v, u),
Rot(u) * Rot(v) + Div(u) * Div(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_1():
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, y, v, u), Dot(Grad(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_2():
print('============== test_1d_scalar_2 ================')
# ... define the weak formulation
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
alpha = Constant('alpha')
nu = Constant('nu')
a = Lambda((x, v, u), alpha * Dot(Grad(u), Grad(v)) + nu * 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_2',
a,
V,
d_constants={'nu': 0.1},
d_args={'alpha': 'double'},
backend='python')
kernel_f90 = compile_kernel('kernel_scalar_2',
a,
V,
d_constants={'nu': 0.1},
d_args={'alpha': 'double'},
backend='fortran')
M_py = assemble_matrix(V, kernel_py, args={'alpha': 2.0})
M_f90 = assemble_matrix(V, kernel_f90, args={'alpha': 2.0})
# ...
assert_identical_coo(M_py, M_f90)
def test_1d_scalar_2():
print('============== test_1d_scalar_2 ================')
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
b = Constant('b')
a = Lambda((x, v, u), Dot(Grad(b * u), Grad(v)) + u * v)
print('> input := {0}'.format(a))
# ... 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)
# ...
# ... 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_2',
a,
V,
d_constants={'b': 0.1},
backend='fortran')
# ...
# ... example of symbol evaluation
t1 = linspace(-pi, pi, ne + 1)
x1 = linspace(0., 1., ne + 1)
e = zeros(ne + 1)
symbol_f90(x1, t1, e)
# ...
print('')
def test_1d_4():
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
b = Function('b')
a = Lambda((x,v,u), Dot(Grad(u), Grad(v)) + b(x)*u*v)
print('> input := {0}'.format(a))
# ...
expr = construct_weak_form(a, dim=DIM)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_3d_scalar_5():
print('============== test_3d_scalar_5 ================')
# ... define the weak formulation
x, y, z = symbols('x y z')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, y, z, v, u),
dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v)) +
dz(dz(u)) * dz(dz(v)) + Dot(Grad(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, nderiv=2)
V2 = SplineSpace(p2, grid=grid_2, nderiv=2)
V3 = SplineSpace(p3, grid=grid_3, nderiv=2)
V = TensorFemSpace(V1, V2, V3)
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_5', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_scalar_5', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py)
M_f90 = assemble_matrix(V, kernel_f90)
# ...
assert_identical_coo(M_py, M_f90)
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 = construct_weak_form(a, dim=DIM, is_block=False)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_1d_2():
x,y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
# b = Function('b')
b = Constant('b')
a = Lambda((x,y,v,u), Dot(Grad(b*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_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_scalar_6():
print('============== test_2d_scalar_6 ================')
# ... define the weak formulation
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, y, v, u),
dx(dx(u)) * dx(dx(v)) + dy(dy(u)) * dy(dy(v)) +
Dot(Grad(u), Grad(v)) + u * v)
# ...
# ... 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, nderiv=2)
V2 = SplineSpace(p2, grid=grid_2, nderiv=2)
V = TensorFemSpace(V1, V2)
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_6', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_scalar_6', a, V, backend='fortran')
M_py = assemble_matrix(V, kernel_py)
M_f90 = assemble_matrix(V, kernel_f90)
# ...
assert_identical_coo(M_py, M_f90)
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('')
def test_2d_block_2():
print('============== test_2d_block_2 ================')
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
epsilon = Constant('epsilon')
Laplace = lambda v, u: Dot(Grad(v), Grad(u))
Mass = lambda v, u: v * u
u1, u2, p = symbols('u1 u2 p')
v1, v2, q = symbols('v1 v2 q')
a = Lambda((x, y, v1, v2, q, u1, u2, p),
Laplace(v1, u1) - dx(v1) * p + Laplace(v2, u2) - dy(v2) * p +
q * (dx(u1) + dy(u2)) + epsilon * Mass(q, p))
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)
V = VectorFemSpace(V, V, V)
# ...
# ... create a glt symbol from a string without evaluation
expr = glt_symbol(a, space=V)
print('> glt symbol := {0}'.format(expr))
# ...
# TODO not working yet => need complex numbers
# # ...
# symbol_f90 = compile_symbol('symbol_block_2', a, V,
# d_constants={'epsilon': 0.1},
# 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((2, 2, ne1+1, ne2+1), order='F')
# symbol_f90(x1,x2,t1,t2, e)
# # ...
print('')
def test_2d_scalar_3():
print('============== test_2d_scalar_3 ================')
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
b = Function('b')
a = Lambda((x, y, v, u), Dot(Grad(u), Grad(v)) + b(x, y) * 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))
# ...
# ... user defined function
def b(x, y):
r = 1. + x * y
return r
# ...
# ... create an interactive pyccel context
from pyccel.epyccel import ContextPyccel
context = ContextPyccel(name='context_scalar_3')
context.insert_function(b, ['double', 'double'],
kind='function',
results=['double'])
context.compile()
# ...
# ...
symbol_f90 = compile_symbol('symbol_scalar_3',
a,
V,
context=context,
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_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_2d_scalar_3():
print('============== test_2d_scalar_3 ================')
# ... define the weak formulation
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
b = Function('b')
a = Lambda((x, y, v, u), Dot(Grad(u), Grad(v)) + b(x, y) * u * v)
# ...
# ... 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)
# ...
# ... user defined function
def b(x, y):
r = 1. + x * (1. - x) + y * (1. - y)
return r
# ...
# ... create an interactive pyccel context
from pyccel.epyccel import ContextPyccel
context = ContextPyccel(name='context_3')
context.insert_function(b, ['double', 'double'],
kind='function',
results=['double'])
context.compile()
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_3',
a,
V,
context=context,
verbose=True,
backend='python')
kernel_f90 = compile_kernel('kernel_scalar_3',
a,
V,
context=context,
verbose=True,
backend='fortran')
# ...
# ...
M_py = assemble_matrix(V, kernel_py)
M_f90 = assemble_matrix(V, kernel_f90)
# ...
assert_identical_coo(M_py, M_f90)
def test_1d_scalar_3():
print('============== test_1d_scalar_3 ================')
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
b = Function('b')
a = Lambda((x, v, u), Dot(Grad(u), Grad(v)) + b(x) * u * v)
print('> input := {0}'.format(a))
# ... 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)
# ...
# ... user defined function
def b(s):
r = 1. + s * (1. - s)
return r
# ...
# ... create an interactive pyccel context
from pyccel.epyccel import ContextPyccel
context = ContextPyccel(name='context_3')
context.insert_function(b, ['double'], kind='function', results=['double'])
context.compile()
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_3',
a,
V,
context=context,
verbose=True,
backend='python')
kernel_f90 = compile_kernel('kernel_scalar_3',
a,
V,
context=context,
verbose=True,
backend='fortran')
# ...
# ...
M_py = assemble_matrix(V, kernel_py)
M_f90 = assemble_matrix(V, kernel_f90)
# ...
assert_identical_coo(M_py, M_f90)
print('')
def test_2d_scalar_2():
print('============== test_2d_scalar_2 ================')
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
c = Constant('c')
b0 = Constant('b0')
b1 = Constant('b1')
b = Tuple(b0, b1)
a = Lambda((x, y, v, u),
c * u * v + Dot(b, Grad(v)) * u + Dot(b, Grad(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_2',
a,
V,
d_constants={
'b0': 0.1,
'b1': 1.,
'c': 0.2
},
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('')