def test_pdes_3d_1():
print('============ test_pdes_3d_1 =============')
# ... abstract model
V = H1Space('V', ldim=3)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
a = BilinearForm((v, u), dot(grad(v), grad(u)))
# ...
# ... discretization
# Input data: degree, number of elements
p1 = 1
p2 = 1
p3 = 1
ne1 = 4
ne2 = 4
ne3 = 4
# Create uniform grid
grid_1 = linspace(0., 1., num=ne1 + 1)
grid_2 = linspace(0., 1., num=ne2 + 1)
grid_3 = linspace(0., 1., num=ne3 + 1)
# Create 1D finite element spaces and precompute quadrature data
V1 = SplineSpace(p1, grid=grid_1)
V1.init_fem()
V2 = SplineSpace(p2, grid=grid_2)
V2.init_fem()
V3 = SplineSpace(p3, grid=grid_3)
V3.init_fem()
# Create 2D tensor product finite element space
V = TensorFemSpace(V1, V2, V3)
# ...
# ...
discretize_symbol(a, [V, V])
# print(mass.symbol.__doc__)
# ...
# ...
n1 = 21
n2 = 21
n3 = 21
t1 = linspace(-pi, pi, n1)
t2 = linspace(-pi, pi, n2)
t3 = linspace(-pi, pi, n3)
x1 = linspace(0., 1., n1)
x2 = linspace(0., 1., n2)
x3 = linspace(0., 1., n3)
xs = [x1, x2, x3]
ts = [t1, t2, t3]
e = a.symbol(*xs, *ts)
print('> ', e.min(), e.max())
def test_pdes_2d_2():
print('============ test_pdes_2d_2 =============')
# ... abstract model
V = H1Space('V', ldim=2)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
c = Constant('c', real=True, label='mass stabilization')
a = BilinearForm((v, u), dot(grad(v), grad(u)) + c * v * u)
# ...
# ... discretization
# Input data: degree, number of elements
p1 = 1
p2 = 1
ne1 = 4
ne2 = 4
# Create uniform grid
grid_1 = linspace(0., 1., num=ne1 + 1)
grid_2 = linspace(0., 1., num=ne2 + 1)
# Create 1D finite element spaces and precompute quadrature data
V1 = SplineSpace(p1, grid=grid_1)
V1.init_fem()
V2 = SplineSpace(p2, grid=grid_2)
V2.init_fem()
# Create 2D tensor product finite element space
V = TensorFemSpace(V1, V2)
# ...
# ...
discretize_symbol(a, [V, V])
# print(mass.symbol.__doc__)
# ...
# ...
n1 = 21
n2 = 21
t1 = linspace(-pi, pi, n1)
t2 = linspace(-pi, pi, n2)
x1 = linspace(0., 1., n1)
x2 = linspace(0., 1., n2)
xs = [x1, x2]
ts = [t1, t2]
e = a.symbol(*xs, *ts, 0.25)
print('> c = 0.25 :: ', e.min(), e.max())
e = a.symbol(*xs, *ts, 0.6)
print('> c = 0.6 :: ', e.min(), e.max())
def test_gelatize_2d_4():
print('============ test_gelatize_2d_4 =============')
V = H1Space('V', ldim=2)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
expr = BilinearForm((v, u), dot(grad(v), grad(u)))
print('> input >>> {0}'.format(expr))
print('> gelatized >>> {0}'.format(gelatize(expr)))
def test_symbol_3d_2():
print('============ test_symbol_3d_2 =============')
# ... abstract model
V = H1Space('V', ldim=3)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
mass = BilinearForm((v, u), u * v)
laplace = BilinearForm((v, u), dot(grad(v), grad(u)))
# ...
# ...
degrees = [1, 1, 1]
symbol = compile_symbol('mass_symbol', mass, degrees)
# ...
# ...
n1 = 21
n2 = 21
n3 = 21
t1 = linspace(-pi, pi, n1)
t2 = linspace(-pi, pi, n2)
t3 = linspace(-pi, pi, n3)
x1 = linspace(0., 1., n1)
x2 = linspace(0., 1., n2)
x3 = linspace(0., 1., n3)
xs = [x1, x2, x3]
ts = [t1, t2, t3]
e = zeros((n1, n2, n3))
# ...
# ...
n_elements = [4, 4, 4]
symbol(*xs, *ts, e, *n_elements)
print('> ', e.min(), e.max())
# ...
# ...
n_elements = [4, 8, 8]
symbol(*xs, *ts, e, *n_elements)
print('> ', e.min(), e.max())
def test_pdes_1d_1():
print('============ test_pdes_1d_1 =============')
# ... abstract model
V = H1Space('V', ldim=1)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
a = BilinearForm((v,u), dot(grad(v), grad(u)))
# ...
# ... discretization
# Input data: degree, number of elements
p1 = 1
ne1 = 4
# Create uniform grid
grid_1 = linspace( 0., 1., num=ne1+1 )
# Create 1D finite element spaces and precompute quadrature data
V = SplineSpace( p1, grid=grid_1 ); V.init_fem()
# ...
# ...
discretize_symbol( a, [V,V] )
# print(mass.symbol.__doc__)
# ...
# ...
n1 = 21
t1 = linspace(-pi, pi, n1)
x1 = linspace(0.,1., n1)
xs = [x1]
ts = [t1]
e = a.symbol(*xs, *ts)
print('> ', e.min(), e.max())
def test_gelatize_1d_1():
print('============ test_gelatize_1d_1 =============')
V = H1Space('V', ldim=1)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
nx = symbols('nx', integer=True)
px = symbols('px', integer=True)
tx = symbols('tx')
c1 = Constant('c1')
c2 = Constant('c2')
c3 = Constant('c3')
c4 = Constant('c4')
# ...
expected = Mass(px, tx) / nx
assert (gelatize(BilinearForm((v, u), u * v)) == expected)
# ...
# ...
expected = nx * Stiffness(px, tx)
assert (gelatize(BilinearForm((v, u), dot(grad(v), grad(u)))) == expected)
# ...
# ...
expected = I * Advection(px, tx)
assert (gelatize(BilinearForm((v, u), dx(u) * v)) == expected)
# ...
# ...
expected = c1 * Mass(px, tx) / nx + c2 * I * Advection(
px, tx) - c3 * I * Advection(px, tx) + c4 * nx * Stiffness(px, tx)
assert (gelatize(
BilinearForm((v, u), c1 * v * u + c2 * dx(u) * v + c3 * dx(v) * u +
c4 * dx(v) * dx(u))) == expected)
def test_symbol_2d_1():
print('============ test_symbol_2d_1 =============')
# ... abstract model
V = H1Space('V', ldim=2)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
mass = BilinearForm((v, u), u * v)
laplace = BilinearForm((v, u), dot(grad(v), grad(u)))
# ...
# ...
degrees = [1, 1]
n_elements = [4, 4]
symbol = compile_symbol('mass_symbol',
mass,
degrees,
n_elements=n_elements)
# ...
# ...
n1 = 101
n2 = 101
t1 = linspace(-pi, pi, n1)
t2 = linspace(-pi, pi, n2)
x1 = linspace(0., 1., n1)
x2 = linspace(0., 1., n2)
xs = [x1, x2]
ts = [t1, t2]
e = zeros((n1, n2))
symbol(*xs, *ts, e)
print('> ', e.min(), e.max())
def test_gelatize_3d_1():
print('============ test_gelatize_3d_1 =============')
V = H1Space('V', ldim=3)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
nx, ny, nz = symbols('nx ny nz', integer=True)
px, py, pz = symbols('px py pz', integer=True)
tx, ty, tz = symbols('tx ty tz')
c = Constant('c')
bx = Constant('bx')
by = Constant('by')
bz = Constant('bz')
b = Tuple(bx, by, bz)
# ...
expected = Mass(px, tx) * Mass(py, ty) * Mass(pz, tz) / (nx * ny * nz)
assert (gelatize(BilinearForm((v, u), u * v)) == expected)
# ...
# ...
expected = nx * Mass(py, ty) * Mass(pz, tz) * Stiffness(px, tx) / (ny * nz)
assert (gelatize(BilinearForm((v, u), dx(u) * dx(v))) == expected)
# ...
# ...
expected = I * Advection(py, ty) * Mass(px, tx) * Mass(pz, tz) / (nx * nz)
assert (gelatize(BilinearForm((v, u), dy(u) * v)) == expected)
# ...
# ...
expected = I * Advection(px, tx) * Mass(py, ty) * Mass(pz, tz) / (ny * nz)
assert (gelatize(BilinearForm((v, u), dx(u) * v)) == expected)
# ...
# ...
expected = (nx * Mass(py, ty) * Mass(pz, tz) * Stiffness(px, tx) /
(ny * nz) +
ny * Mass(px, tx) * Mass(pz, tz) * Stiffness(py, ty) /
(nx * nz) +
nz * Mass(px, tx) * Mass(py, ty) * Stiffness(pz, tz) /
(nx * ny))
assert (gelatize(BilinearForm((v, u), dot(grad(v), grad(u)))) == expected)
# ...
# ...
expected = (
nx * Mass(py, ty) * Mass(pz, tz) * Stiffness(px, tx) / (ny * nz) +
I * Advection(px, tx) * Mass(py, ty) * Mass(pz, tz) / (ny * nz) +
ny * Mass(px, tx) * Mass(pz, tz) * Stiffness(py, ty) / (nx * nz) +
I * Advection(py, ty) * Mass(px, tx) * Mass(pz, tz) / (nx * nz) +
nz * Mass(px, tx) * Mass(py, ty) * Stiffness(pz, tz) / (nx * ny))
assert (gelatize(
BilinearForm(
(v, u),
dot(grad(v), grad(u)) + dx(u) * v + dy(u) * v)) == expected)
# ...
# ...
expected = (-bx * I * Advection(px, tx) * Mass(py, ty) * Mass(pz, tz) /
(ny * nz) -
by * I * Advection(py, ty) * Mass(px, tx) * Mass(pz, tz) /
(nx * nz) -
bz * I * Advection(pz, tz) * Mass(px, tx) * Mass(py, ty) /
(nx * ny))
assert (gelatize(BilinearForm((v, u), dot(b, grad(v)) * u)) == expected)
# ...
# ...
expected = (bx**2 * nx * Mass(py, ty) * Mass(pz, tz) * Stiffness(px, tx) /
(ny * nz) + 2 * bx * by * Advection(px, tx) *
Advection(py, ty) * Mass(pz, tz) / nz + 2 * bx * bz *
Advection(px, tx) * Advection(pz, tz) * Mass(py, ty) / ny +
by**2 * ny * Mass(px, tx) * Mass(pz, tz) * Stiffness(py, ty) /
(nx * nz) + 2 * by * bz * Advection(py, ty) *
Advection(pz, tz) * Mass(px, tx) / nx +
bz**2 * nz * Mass(px, tx) * Mass(py, ty) * Stiffness(pz, tz) /
(nx * ny))
assert (gelatize(BilinearForm(
(v, u),
dot(b, grad(v)) * dot(b, grad(u)))) == expected)
# ...
degrees = None
# degrees = [2, 1, 1]
# evaluate = True
evaluate = False
def test_gelatize_2d_1():
print('============ test_gelatize_2d_1 =============')
V = H1Space('V', ldim=2)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
nx, ny = symbols('nx ny', integer=True)
px, py = symbols('px py', integer=True)
tx, ty = symbols('tx ty')
c = Constant('c')
bx = Constant('bx')
by = Constant('by')
b = Tuple(bx, by)
# ...
expected = Mass(px, tx) * Mass(py, ty) / (nx * ny)
assert (gelatize(BilinearForm((v, u), u * v)) == expected)
# ...
# ...
expected = Mass(py, ty) * nx * Stiffness(px, tx) / ny
assert (gelatize(BilinearForm((v, u), dx(u) * dx(v))) == expected)
# ...
# ...
expected = I * Advection(py, ty) * Mass(px, tx) / nx
assert (gelatize(BilinearForm((v, u), dy(u) * v)) == expected)
# ...
# ...
expected = I * Advection(px, tx) * Mass(py, ty) / ny
assert (gelatize(BilinearForm((v, u), dx(u) * v)) == expected)
# ...
# ...
expected = Mass(px, tx) * ny * Stiffness(py, ty) / nx + Mass(
py, ty) * nx * Stiffness(px, tx) / ny
assert (gelatize(BilinearForm((v, u), dot(grad(v), grad(u)))) == expected)
# ...
# ...
expected = (nx * Mass(py, ty) * Stiffness(px, tx) / ny +
I * Advection(px, tx) * Mass(py, ty) / ny +
ny * Mass(px, tx) * Stiffness(py, ty) / nx +
I * Advection(py, ty) * Mass(px, tx) / nx)
assert (gelatize(
BilinearForm(
(v, u),
dot(grad(v), grad(u)) + dx(u) * v + dy(u) * v)) == expected)
# ...
# ...
expected = -bx * I * Advection(px, tx) * Mass(
py, ty) / ny - by * I * Advection(py, ty) * Mass(px, tx) / nx
assert (gelatize(BilinearForm((v, u), dot(b, grad(v)) * u)) == expected)
# ...
# ...
expected = bx**2 * nx * Mass(py, ty) * Stiffness(
px, tx) / ny + 2 * bx * by * Advection(px, tx) * Advection(
py, ty) + by**2 * ny * Mass(px, tx) * Stiffness(py, ty) / nx
assert (gelatize(BilinearForm(
(v, u),
dot(b, grad(v)) * dot(b, grad(u)))) == expected)
# ...
degrees = None
# degrees = [2, 1]
# evaluate = True
evaluate = False