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_1d_scalar_5():
print('============== test_1d_scalar_5 ================')
# ... define the weak formulation
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, v, u), dx(dx(u)) * dx(dx(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, nderiv=2)
# ...
# ...
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_3d_scalar_4():
print('============== test_3d_scalar_4 ================')
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)))
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)
V = TensorFemSpace(V1, V2, V3)
# ...
# ... 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)
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((ne1 + 1, ne2 + 1, ne3 + 1), order='F')
symbol_f90(x1, x2, x3, t1, t2, t3, e)
# ...
print('')
def test_1d_3():
x = Symbol('x')
u0, u1 = symbols('u0 u1')
v0, v1 = symbols('v0 v1')
a = Lambda((x,v0,v1,u0,u1), dx(u0)*dx(v0) + dx(u1)*v0 + u0*dx(v1) + u1*v1)
print('> input := {0}'.format(a))
# ...
expr = construct_weak_form(a, dim=DIM, is_block=True)
print('> weak form := {0}'.format(expr))
# ...
print('')
def test_2d_scalar_5():
print('============== test_2d_scalar_5 ================')
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)))
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_5', 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_1d_5():
x,y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x,y,v,u), dx(dx(u))*dx(dx(dx(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_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_1d_block_1():
print('============== test_1d_block_1 ================')
x = Symbol('x')
u0, u1 = symbols('u0 u1')
v0, v1 = symbols('v0 v1')
a = Lambda((x, v0, v1, u0, u1),
dx(u0) * dx(v0) + dx(u1) * v0 + u0 * dx(v1) + u1 * v1)
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)
V1 = SplineSpace(p, grid=grid)
V2 = SplineSpace(p, grid=grid)
V = VectorFemSpace(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_block_1', a, V, backend='fortran')
# ...
# ... example of symbol evaluation
t1 = linspace(-pi, pi, ne + 1)
x1 = linspace(0., 1., ne + 1)
e = zeros((2, 2, ne + 1))
symbol_f90(x1, t1, e)
# ...
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_1d_scalar_4():
print('============== test_1d_scalar_4 ================')
x = Symbol('x')
u = Symbol('u')
v = Symbol('v')
a = Lambda((x, v, u), dx(dx(u)) * dx(dx(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_4', a, V, 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_block_1():
print('============== test_1d_block_1 ================')
# ... define the weak formulation
x = Symbol('x')
u0, u1 = symbols('u0 u1')
v0, v1 = symbols('v0 v1')
a = Lambda((x, v0, v1, u0, u1),
dx(u0) * dx(v0) + dx(u1) * v0 + u0 * dx(v1) + u1 * v1)
# ...
# ... 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)
# ...
# ... Vector fem space
V = VectorFemSpace(V, V)
# ...
# ...
kernel_py = compile_kernel('kernel_block_1', a, V, backend='python')
kernel_f90 = compile_kernel('kernel_block_1', 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_6():
x,y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
F = Field('F')
a = Lambda((x,y,v,u), Dot(Grad(dx(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_2d_scalar_4():
print('============== test_2d_scalar_4 ================')
# ... define the weak formulation
x, y = symbols('x y')
u = Symbol('u')
v = Symbol('v')
b0 = Function('b0')
b1 = Function('b1')
a = Lambda((x, y, v, u), (b0(x, y) * dx(v) + b1(x, y) * dy(v)) *
(b0(x, y) * dx(u) + b1(x, y) * dy(u)))
# ...
# ... 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 b0(x, y):
from numpy import sin
from scipy import pi
r = 1.1659397624413860850012270020670 * (1.0 + 0.1 * sin(2 * pi * y))
return r
def b1(x, y):
from numpy import sin
from scipy import pi
r = 1.0 * (1.0 + 0.1 * sin(2 * pi * y))
return r
# ...
# ... create an interactive pyccel context
from pyccel.epyccel import ContextPyccel
context = ContextPyccel(name='context_4')
context.insert_function(b0, ['double', 'double'],
kind='function',
results=['double'])
context.insert_function(b1, ['double', 'double'],
kind='function',
results=['double'])
context.compile()
# ...
# ...
kernel_py = compile_kernel('kernel_scalar_4',
a,
V,
context=context,
verbose=True,
backend='python')
kernel_f90 = compile_kernel('kernel_scalar_4',
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_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('')