def test_logical_expr_2d_3():
dim = 2
A = Square('A')
B = Square('B')
M1 = Mapping('M1', dim=dim)
M2 = Mapping('M2', dim=dim)
D1 = M1(A)
D2 = M2(B)
domain = D1.join(D2,
name='domain',
bnd_minus=D1.get_boundary(axis=0, ext=1),
bnd_plus=D2.get_boundary(axis=0, ext=-1))
V = VectorFunctionSpace('V', domain, kind='hcurl')
u, v = [element_of(V, name=i) for i in ['u', 'v']]
int_0 = lambda expr: integral(domain, expr)
expr = LogicalExpr(int_0(dot(u, v)), domain)
assert str(
expr.args[0]
) == 'Integral(A, Dot((Jacobian(M1)**(-1)).T * u, (Jacobian(M1)**(-1)).T * v)*sqrt(det(Jacobian(M1).T * Jacobian(M1))))'
assert str(
expr.args[1]
) == 'Integral(B, Dot((Jacobian(M2)**(-1)).T * u, (Jacobian(M2)**(-1)).T * v)*sqrt(det(Jacobian(M2).T * Jacobian(M2))))'
def two_patches():
from sympde.topology import InteriorDomain
from sympde.topology import Connectivity, Interface
A = Square('A')
B = Square('B')
A = A.interior
B = B.interior
connectivity = Connectivity()
bnd_A_1 = Boundary(r'\Gamma_1', A, axis=0, ext=-1)
bnd_A_2 = Boundary(r'\Gamma_2', A, axis=0, ext=1)
bnd_A_3 = Boundary(r'\Gamma_3', A, axis=1, ext=-1)
bnd_A_4 = Boundary(r'\Gamma_4', A, axis=1, ext=1)
bnd_B_1 = Boundary(r'\Gamma_1', B, axis=0, ext=-1)
bnd_B_2 = Boundary(r'\Gamma_2', B, axis=0, ext=1)
bnd_B_3 = Boundary(r'\Gamma_3', B, axis=1, ext=-1)
bnd_B_4 = Boundary(r'\Gamma_4', B, axis=1, ext=1)
connectivity['I'] = Interface('I', bnd_A_2, bnd_B_1)
Omega = Domain('Omega',
interiors=[A, B],
boundaries=[
bnd_A_1, bnd_A_2, bnd_A_3, bnd_A_4, bnd_B_1,
bnd_B_2, bnd_B_3, bnd_B_4
],
connectivity=connectivity)
return Omega
def test_square():
square = Square('square')
assert (square.dim == 2)
assert (len(square.boundary) == 4)
square.export('square.h5')
# read it again
D = Domain.from_file('square.h5')
def test_system_2d():
domain = Square()
V = FunctionSpace('V', domain)
x, y = V.coordinates
u, v, p, q = [TestFunction(V, name=i) for i in ['u', 'v', 'p', 'q']]
a1, a2, b1, b2 = [Constant(i, real=True) for i in ['a1', 'a2', 'b1', 'b2']]
# ...
a = BilinearForm((v, u), dot(grad(u), grad(v)))
m = BilinearForm((v, u), u * v)
expr = a(p, u) + a1 * m(p, u) + b1 * m(p, v) + a(
q, v) + a2 * m(q, u) + b2 * m(q, v)
b = BilinearForm(((p, q), (u, v)), expr)
print(evaluate(b, verbose=True))
# ...
# ...
f1 = x * y
f2 = x + y
l1 = LinearForm(p, f1 * p)
l2 = LinearForm(q, f2 * q)
expr = l1(p) + l2(q)
l = LinearForm((p, q), expr)
print(evaluate(l, verbose=True))
def test_calls_2d_3():
domain = Square()
V = FunctionSpace('V', domain)
x, y = domain.coordinates
pn = Field('pn', V)
wn = Field('wn', V)
dp = TestFunction(V, name='dp')
dw = TestFunction(V, name='dw')
tau = TestFunction(V, name='tau')
sigma = TestFunction(V, name='sigma')
Re = Constant('Re', real=True)
dt = Constant('dt', real=True)
alpha = Constant('alpha', real=True)
l1 = LinearForm(tau,
bracket(pn, wn) * tau - 1. / Re * dot(grad(tau), grad(wn)))
# ...
l = LinearForm((tau, sigma), dt * l1(tau))
print(evaluate(l, verbose=True))
def test_terminal_expr_linear_2d_5(boundary=[r'\Gamma_1', r'\Gamma_3']):
# ... abstract model
domain = Square()
V = ScalarFunctionSpace('V', domain)
B_neumann = [domain.get_boundary(i) for i in boundary]
if len(B_neumann) == 1:
B_neumann = B_neumann[0]
else:
B_neumann = Union(*B_neumann)
x, y = domain.coordinates
nn = NormalVector('nn')
F = element_of(V, name='F')
v = element_of(V, name='v')
u = element_of(V, name='u')
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(B_neumann, expr)
expr = dot(grad(v), grad(u))
a = BilinearForm((v, u), int_0(expr))
solution = cos(0.5 * pi * x) * cos(0.5 * pi * y)
f = (1. / 2.) * pi**2 * solution
expr = f * v
l0 = LinearForm(v, int_0(expr))
expr = v * dot(grad(solution), nn)
l_B_neumann = LinearForm(v, int_1(expr))
expr = l0(v) + l_B_neumann(v)
l = LinearForm(v, expr)
print(TerminalExpr(l))
print('')
def test_interface_integral_1():
# ...
A = Square('A')
B = Square('B')
domain = A.join(B,
name='domain',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, v = elements_of(V, names='u, v')
# ...
I = domain.interfaces
# ...
# expr = minus(Dn(u))
# print(expr)
# import sys; sys.exit(0)
# ... bilinear forms
# a = BilinearForm((u,v), integral(domain, u*v))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v))))
# a = BilinearForm((u,v), integral(I, jump(u) * jump(v)))
# a = BilinearForm((u,v), integral(I, jump(Dn(u)) * jump(v)))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v)))
# + integral(I, jump(u) * jump(v)))
# Nitsch
kappa = Constant('kappa')
expr_I = (-jump(u) * jump(Dn(v)) + kappa * jump(u) * jump(v) +
plus(Dn(u)) * minus(v) + minus(Dn(u)) * plus(v))
a = BilinearForm(
(u, v),
integral(domain, dot(grad(u), grad(v))) + integral(I, expr_I))
# # TODO BUG
# bnd_A = A.get_boundary(axis=0, ext=1)
#
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v)))
# + integral(I, jump(u) * jump(v))
# + integral(bnd_A, dx(u)*v))
expr = TerminalExpr(a)
print(expr)
def test_rectangle():
# Create 2D rectangular domain [1, 5] X [3, 7]
domain = Square('rectangle', bounds1=(1, 5), bounds2=(3, 7))
assert isinstance(domain, Square)
# BasicDomain's attributes
assert domain.dim == 2
assert domain.name == 'rectangle'
assert domain.coordinates == (x1, x2)
# Domain's attributes
assert isinstance(domain.interior, InteriorDomain)
assert isinstance(domain.interior.target, ProductDomain)
assert all(isinstance(i, Interval) for i in domain.interior.target.domains)
assert len(domain.interior.target.domains) == 2
assert len(domain.boundary) == 4
assert domain.dtype == {
'type': 'Square',
'parameters': {
'bounds1': [1, 5],
'bounds2': [3, 7]
}
}
# NCube's attributes
assert domain.min_coords == (1, 3)
assert domain.max_coords == (5, 7)
# Square's attributes
assert domain.bounds1 == (1, 5)
assert domain.bounds2 == (3, 7)
# Export to file, read it again and compare with original domain
domain.export('domain.h5')
D = Domain.from_file('domain.h5')
assert D.logical_domain == domain
def test_unit_square():
# Create 2D square domain [0, 1]^2
domain = Square('square')
assert isinstance(domain, Square)
# BasicDomain's attributes
assert domain.dim == 2
assert domain.name == 'square'
assert domain.coordinates == (x1, x2)
# Domain's attributes
assert isinstance(domain.interior, InteriorDomain)
assert isinstance(domain.interior.target, ProductDomain)
assert all(isinstance(i, Interval) for i in domain.interior.target.domains)
assert len(domain.interior.target.domains) == 2
assert len(domain.boundary) == 4
assert domain.dtype == {
'type': 'Square',
'parameters': {
'bounds1': [0, 1],
'bounds2': [0, 1]
}
}
# NCube's attributes
assert domain.min_coords == (0, 0)
assert domain.max_coords == (1, 1)
# Square's attributes
assert domain.bounds1 == (0, 1)
assert domain.bounds2 == (0, 1)
# Export to file, read it again and compare with original domain
domain.export('domain.h5')
D = Domain.from_file('domain.h5')
assert D.logical_domain == domain
def test_interface_integral_2():
# ...
A = Square('A')
B = Square('B')
domain = A.join(B,
name='domain',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, u1, u2, u3 = elements_of(V, names='u, u1, u2, u3')
v, v1, v2, v3 = elements_of(V, names='v, v1, v2, v3')
# ...
I = domain.interfaces
a = BilinearForm((u, v), integral(domain, dot(grad(u), grad(v))))
b = BilinearForm((u, v), integral(I, jump(u) * jump(v)))
A = BilinearForm(((u1, u2), (v1, v2)),
a(u1, v1) + a(u2, v2) + b(u1, v1) + b(u2, v2) + b(u1, v2))
B = BilinearForm(
((u1, u2, u3), (v1, v2, v3)),
a(u1, v1) + a(u2, v2) + a(u3, v3) + b(u1, v1) + b(u2, v2) + b(u1, v2))
print(TerminalExpr(A))
print(TerminalExpr(B))
# ...
# ... linear forms
b = LinearForm(v, integral(I, jump(v)))
b = LinearForm((v1, v2), b(v1) + b(v2))
expr = TerminalExpr(b)
print(expr)
def test_equation_2d_5():
domain = Square()
x, y = domain.coordinates
f0 = Matrix([
2 * pi**2 * sin(pi * x) * sin(pi * y),
2 * pi**2 * sin(pi * x) * sin(pi * y)
])
f1 = cos(pi * x) * cos(pi * y)
W = VectorFunctionSpace('W', domain)
V = ScalarFunctionSpace('V', domain)
X = ProductSpace(W, V)
F = element_of(W, name='F')
G = element_of(V, name='G')
u, v = [element_of(W, name=i) for i in ['u', 'v']]
p, q = [element_of(V, name=i) for i in ['p', 'q']]
int_0 = lambda expr: integral(domain, expr)
a0 = BilinearForm((v, u), int_0(inner(grad(v), grad(u))))
print(' a0 done.')
a1 = BilinearForm((q, p), int_0(p * q))
print(' a1 done.')
a = BilinearForm(((v, q), (u, p)), a0(v, u) + a1(q, p))
print(' a done.')
l0 = LinearForm(v, int_0(dot(f0, v)))
l1 = LinearForm(q, int_0(f1 * q))
l = LinearForm((v, q), l0(v) + l1(q))
print('****************************')
bc = EssentialBC(u, 0, domain.boundary)
equation = Equation(a, l, tests=[v, q], trials=[u, p], bc=bc)
# ...
print('=======')
print(equation.lhs.expr)
print('')
# ...
# ...
print('=======')
print(equation.rhs.expr)
print('')
def test_bilinearity_2d_1():
domain = Square()
x, y = domain.coordinates
alpha = Constant('alpha')
beta = Constant('beta')
f1 = x * y
f2 = x + y
f = Tuple(f1, f2)
V = FunctionSpace('V', domain)
# TODO improve: naming are not given the same way
G = Field('G', V)
p, q = [TestFunction(V, name=i) for i in ['p', 'q']]
#####################################
# linear expressions
#####################################
# ...
expr = p * q
assert (is_bilinear_form(expr, (p, q)))
# ...
# ...
expr = dot(grad(p), grad(q))
assert (is_bilinear_form(expr, (p, q)))
# ...
# ...
expr = alpha * dot(grad(p),
grad(q)) + beta * p * q + laplace(p) * laplace(q)
assert (is_bilinear_form(expr, (p, q)))
# ...
#####################################
#####################################
# nonlinear expressions
#####################################
# ...
with pytest.raises(UnconsistentLinearExpressionError):
expr = alpha * dot(grad(p**2), grad(q)) + beta * p * q
is_bilinear_form(expr, (p, q))
def test_curldiv_2d():
domain = Square()
W1 = VectorFunctionSpace('W1', domain)
T1 = VectorFunctionSpace('T1', domain)
w1 = VectorTestFunction(W1, name='w1')
t1 = VectorTestFunction(T1, name='t1')
mu = Constant('mu')
# ...
a = BilinearForm((w1, t1),
rot(w1) * rot(t1) + mu * div(w1) * div(t1),
name='a')
print(a)
print(atomize(a))
print(evaluate(a))
def test_calls_2d_2():
domain = Square()
V = FunctionSpace('V', domain)
x, y = V.coordinates
u, v = [TestFunction(V, name=i) for i in ['u', 'v']]
Un = Field('Un', V)
# ...
a = BilinearForm((v, u), dot(grad(u), grad(v)))
expr = a(v, Un)
print(evaluate(expr, verbose=True))
# ...
# ...
l = LinearForm(v, a(v, Un))
print(evaluate(l, verbose=True))
def test_equation_2d_2():
domain = Square()
V = ScalarFunctionSpace('V', domain)
x, y = domain.coordinates
pn, wn = [element_of(V, name=i) for i in ['pn', 'wn']]
dp = element_of(V, name='dp')
dw = element_of(V, name='dw')
tau = element_of(V, name='tau')
sigma = element_of(V, name='sigma')
Re = Constant('Re', real=True)
dt = Constant('dt', real=True)
alpha = Constant('alpha', real=True)
int_0 = lambda expr: integral(domain, expr)
s = BilinearForm((tau, sigma), int_0(dot(grad(tau), grad(sigma))))
m = BilinearForm((tau, sigma), int_0(tau * sigma))
b1 = BilinearForm((tau, dw), int_0(bracket(pn, dw) * tau))
b2 = BilinearForm((tau, dp), int_0(bracket(dp, wn) * tau))
l1 = LinearForm(
tau, int_0(bracket(pn, wn) * tau - 1. / Re * dot(grad(tau), grad(wn))))
expr = m(tau, dw) - alpha * dt * b1(tau, dw) - dt * b2(
tau, dp) - (alpha * dt / Re) * s(tau, dw)
a = BilinearForm(((tau, sigma), (dp, dw)), int_0(expr))
l = LinearForm((tau, sigma), dt * l1(tau))
bc = [EssentialBC(dp, 0, domain.boundary)]
bc += [EssentialBC(dw, 0, domain.boundary)]
equation = Equation(a, l, tests=[tau, sigma], trials=[dp, dw], bc=bc)
def test_evaluation_2d_2():
domain = Square()
x, y = domain.coordinates
f0 = Tuple(2 * pi**2 * sin(pi * x) * sin(pi * y),
2 * pi**2 * sin(pi * x) * sin(pi * y))
f1 = cos(pi * x) * cos(pi * y)
W = VectorFunctionSpace('W', domain)
V = FunctionSpace('V', domain)
X = ProductSpace(W, V)
# TODO improve: naming are not given the same way
F = VectorField(W, name='F')
G = Field('G', V)
u, v = [VectorTestFunction(W, name=i) for i in ['u', 'v']]
p, q = [TestFunction(V, name=i) for i in ['p', 'q']]
a0 = BilinearForm((v, u), inner(grad(v), grad(u)))
a1 = BilinearForm((q, p), p * q)
a = BilinearForm(((v, q), (u, p)), a0(v, u) + a1(q, p))
l0 = LinearForm(v, dot(f0, v))
l1 = LinearForm(q, f1 * q)
l = LinearForm((v, q), l0(v) + l1(q))
# ...
print(a)
print(evaluate(a))
print('')
# ...
# ...
print(l)
print(evaluate(l))
print('')
def test_terminal_expr_linear_2d_3():
domain = Square()
B = domain.boundary
x, y = domain.coordinates
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
nn = NormalVector('nn')
V = ScalarFunctionSpace('V', domain)
u, u1, u2 = [element_of(V, name=i) for i in ['u', 'u1', 'u2']]
v, v1, v2 = [element_of(V, name=i) for i in ['v', 'v1', 'v2']]
# ...
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(B, expr)
l = LinearForm(v, int_1(dot(grad(v), nn)))
print(TerminalExpr(l))
print('')
def test_logical_expr_2d_2():
dim = 2
A = Square('A')
B = Square('B')
M1 = Mapping('M1', dim=dim)
M2 = Mapping('M2', dim=dim)
D1 = M1(A)
D2 = M2(B)
domain = D1.join(D2,
name='domain',
bnd_minus=D1.get_boundary(axis=0, ext=1),
bnd_plus=D2.get_boundary(axis=0, ext=-1))
V1 = ScalarFunctionSpace('V1', domain, kind='h1')
V2 = VectorFunctionSpace('V2', domain, kind='h1')
u1, v1 = [element_of(V1, name=i) for i in ['u1', 'v1']]
u2, v2 = [element_of(V2, name=i) for i in ['u2', 'v2']]
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(domain.interfaces, expr)
expr = LogicalExpr(int_0(u1 * v1), domain)
assert str(
expr.args[0]
) == 'Integral(A, u1*v1*sqrt(det(Jacobian(M1).T * Jacobian(M1))))'
assert str(
expr.args[1]
) == 'Integral(B, u1*v1*sqrt(det(Jacobian(M2).T * Jacobian(M2))))'
expr = LogicalExpr(int_1(plus(u1) * plus(v1)), domain)
assert str(
expr
) == 'Integral(A|B, PlusInterfaceOperator(u1)*PlusInterfaceOperator(v1)*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
expr = LogicalExpr(int_1(minus(u1) * minus(v1)), domain)
assert str(
expr
) == 'Integral(A|B, MinusInterfaceOperator(u1)*MinusInterfaceOperator(v1)*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
expr = LogicalExpr(int_0(dot(u2, v2)), domain)
assert str(
expr.args[0]
) == 'Integral(A, Dot(u2, v2)*sqrt(det(Jacobian(M1).T * Jacobian(M1))))'
assert str(
expr.args[1]
) == 'Integral(B, Dot(u2, v2)*sqrt(det(Jacobian(M2).T * Jacobian(M2))))'
expr = LogicalExpr(int_1(dot(plus(u2), plus(v2))), domain)
assert str(
expr
) == 'Integral(A|B, Dot(PlusInterfaceOperator(u2), PlusInterfaceOperator(v2))*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
expr = LogicalExpr(int_1(dot(minus(u2), minus(v2))), domain)
assert str(
expr
) == 'Integral(A|B, Dot(MinusInterfaceOperator(u2), MinusInterfaceOperator(v2))*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
expr = LogicalExpr(int_1(dot(grad(minus(u2)), grad(minus(v2)))), domain)
assert str(
expr
) == 'Integral(A|B, Dot((Jacobian(M1)**(-1)).T * Grad(MinusInterfaceOperator(u2)), (Jacobian(M1)**(-1)).T * Grad(MinusInterfaceOperator(v2)))*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
expr = LogicalExpr(int_1(dot(grad(plus(u2)), grad(plus(v2)))), domain)
assert str(
expr
) == 'Integral(A|B, Dot((Jacobian(M2)**(-1)).T * Grad(PlusInterfaceOperator(u2)), (Jacobian(M2)**(-1)).T * Grad(PlusInterfaceOperator(v2)))*sqrt(det(Jacobian(M1|M2).T * Jacobian(M1|M2))))'
def test_domain_join_square():
# ... line
A = Square('A')
B = Square('B')
C = Square('C')
# ...
# ...
AB = A.join(B, name = 'AB',
bnd_minus = A.get_boundary(axis=0, ext=1),
bnd_plus = B.get_boundary(axis=0, ext=-1))
print(AB)
print(AB.interior)
print(AB.interfaces)
print(AB.connectivity)
print('')
# ...
# ...
AB = A.join(B, name = 'AB',
bnd_minus = A.get_boundary(axis=0, ext=1),
bnd_plus = B.get_boundary(axis=0, ext=-1))
ABC = AB.join(C, name = 'ABC',
bnd_minus = B.get_boundary(axis=0, ext=1),
bnd_plus = C.get_boundary(axis=0, ext=-1))
print(ABC)
print(ABC.interior)
print(ABC.interfaces)
print(list(ABC.connectivity.items()))
print('')
def test_domain_join_square():
# ... line
A = Square('A')
B = Square('B')
C = Square('C')
# ...
# ...
AB_bnd_minus = A.get_boundary(axis=0, ext=1)
AB_bnd_plus = B.get_boundary(axis=0, ext=-1)
AB = A.join(B, name = 'AB',
bnd_minus = AB_bnd_minus,
bnd_plus = AB_bnd_plus)
print(AB)
assert AB.interior == Union(A.interior, B.interior)
assert AB.interfaces == Interface('A|B', AB_bnd_minus, AB_bnd_plus)
print(AB.connectivity)
# ...
BC_bnd_minus = B.get_boundary(axis=0, ext=1)
BC_bnd_plus = C.get_boundary(axis=0, ext=-1)
ABC = AB.join(C, name = 'ABC',
bnd_minus = BC_bnd_minus,
bnd_plus = BC_bnd_plus)
print(ABC)
assert ABC.interior == Union(A.interior, B.interior, C.interior)
assert ABC.interfaces == Union(Interface('A|B', AB_bnd_minus, AB_bnd_plus),Interface('B|C', BC_bnd_minus, BC_bnd_plus))
print(list(ABC.connectivity.items()))
print('')
def test_equation_2d_6():
domain = Square()
x, y = domain.coordinates
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
b1 = 1.
b2 = 0.
b = Tuple(b1, b2)
# right hand side
f = x * y
e = ElementDomain()
area = Area(e)
V = ScalarFunctionSpace('V', domain)
u, v = [element_of(V, name=i) for i in ['u', 'v']]
int_0 = lambda expr: integral(domain, expr)
# ...
expr = kappa * dot(grad(u), grad(v)) + dot(b, grad(u)) * v
a = BilinearForm((v, u), int_0(expr))
# ...
# ...
expr = f * v
l0 = LinearForm(v, int_0(expr))
# ...
# ...
expr = (-kappa * laplace(u) + dot(b, grad(u))) * dot(b, grad(v))
s1 = BilinearForm((v, u), int_0(expr))
expr = -f * dot(b, grad(v))
l1 = LinearForm(v, int_0(expr))
# ...
# ...
expr = (-kappa * laplace(u) + dot(b, grad(u))) * (dot(b, grad(v)) -
kappa * laplace(v))
s2 = BilinearForm((v, u), int_0(expr))
expr = -f * (dot(b, grad(v)) - kappa * laplace(v))
l2 = LinearForm(v, int_0(expr))
# ...
# ...
expr = (-kappa * laplace(u) + dot(b, grad(u))) * (dot(b, grad(v)) +
kappa * laplace(v))
s3 = BilinearForm((v, u), int_0(expr))
expr = -f * (dot(b, grad(v)) + kappa * laplace(v))
l3 = LinearForm(v, int_0(expr))
# ...
# ...
expr = a(v, u) + mu * area * s1(v, u)
a1 = BilinearForm((v, u), expr)
# ...
# ...
expr = a(v, u) + mu * area * s2(v, u)
a2 = BilinearForm((v, u), expr)
# ...
# ...
expr = a(v, u) + mu * area * s3(v, u)
a3 = BilinearForm((v, u), expr)
# ...
bc = EssentialBC(u, 0, domain.boundary)
# ...
l = LinearForm(v, l0(v) + mu * area * l1(v))
eq_1 = Equation(a1, l, tests=v, trials=u, bc=bc)
# ...
# ...
l = LinearForm(v, l0(v) + mu * area * l2(v))
eq_2 = Equation(a2, l, tests=v, trials=u, bc=bc)
# ...
# ...
l = LinearForm(v, l0(v) + mu * area * l3(v))
eq_3 = Equation(a3, l, tests=v, trials=u, bc=bc)
def test_terminal_expr_bilinear_2d_3():
domain = Square()
V = ScalarFunctionSpace('V', domain)
B = domain.boundary
v = element_of(V, name='v')
u = element_of(V, name='u')
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
nn = NormalVector('nn')
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(B, expr)
# nitsche
a0 = BilinearForm((u, v), int_0(dot(grad(v), grad(u))))
a_B = BilinearForm((u,v), int_1(-u*dot(grad(v), nn) \
-v*dot(grad(u), nn) \
+kappa*u*v))
a = BilinearForm((u, v), a0(u, v) + a_B(u, v))
print(TerminalExpr(a))
print('')
a = BilinearForm(
(u, v),
int_0(u * v + dot(grad(u), grad(v))) + int_1(v * dot(grad(u), nn)))
print(TerminalExpr(a))
print('')
# ...
# ...
a = BilinearForm((u, v), int_0(u * v))
print(TerminalExpr(a))
print('')
# ...
# ...
a1 = BilinearForm((u, v), int_0(u * v))
a = BilinearForm((u, v), a1(u, v))
print(TerminalExpr(a))
print('')
# ...
# ...
a1 = BilinearForm((u, v), int_0(u * v))
a2 = BilinearForm((u, v), int_0(dot(grad(u), grad(v))))
a = BilinearForm((u, v), a1(u, v) + a2(u, v))
print(TerminalExpr(a))
print('')
# ...
# ...
a1 = BilinearForm((u, v), int_0(u * v))
a2 = BilinearForm((u, v), int_0(dot(grad(u), grad(v))))
a = BilinearForm((u, v), a1(u, v) + kappa * a2(u, v))
print(TerminalExpr(a))
print('')
# ...
# ...
a1 = BilinearForm((u, v), int_0(u * v))
a2 = BilinearForm((u, v), int_0(dot(grad(u), grad(v))))
a3 = BilinearForm((u, v), int_1(v * dot(grad(u), nn)))
a = BilinearForm((u, v), a1(u, v) + kappa * a2(u, v) + mu * a3(u, v))
print(TerminalExpr(a))
print('')
from nodes import CoefficientBasis
from nodes import StencilMatrixLocalBasis
from nodes import StencilVectorLocalBasis
from nodes import StencilMatrixGlobalBasis
from nodes import StencilVectorGlobalBasis
from nodes import ElementOf
from nodes import WeightedVolumeQuadrature
from nodes import ComputeKernelExpr
from nodes import AST
from nodes import Block
from nodes import Reset
from parser import parse
# ... abstract model
domain = Square()
M = Mapping('M', domain.dim)
V = ScalarFunctionSpace('V', domain)
u,v = elements_of(V, names='u,v')
expr = dot(grad(v), grad(u))
# ...
# ...
grid = Grid()
element = Element()
g_quad = GlobalTensorQuadrature()
l_quad = LocalTensorQuadrature()
quad = TensorQuadrature()
g_basis = GlobalTensorQuadratureTrialBasis(u)
def test_interface_integral_3():
# ...
A = Square('A')
B = Square('B')
C = Square('C')
AB = A.join(B,
name='AB',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
domain = AB.join(C,
name='domain',
bnd_minus=B.get_boundary(axis=0, ext=1),
bnd_plus=C.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, v = elements_of(V, names='u, v')
# ...
I = domain.interfaces
# print(I)
# print(integral(I, jump(u) * jump(v)))
# a = BilinearForm((u,v), integral(domain, u*v))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v))))
# a = BilinearForm((u,v), integral(I, jump(u) * jump(v)))
a = BilinearForm((u, v),
integral(domain, dot(grad(u), grad(v))) +
integral(I,
jump(u) * jump(v)))
expr = TerminalExpr(a)
print(expr)
# ...
# ... linear forms
b = LinearForm(
v,
integral(domain,
sin(x + y) * v) + integral(I,
cos(x + y) * jump(v)))
expr = TerminalExpr(b)
print(expr)