def apply(self, u):
def rhs(x):
z = pi / 2 * (x[0]**2 + x[1]**2 + x[2]**2)
return 2 * pi * (1.5 * sin(z) + z * cos(z)) - 2.0 * exp(cos(z))
return (integrate(lambda x: -n_dot_grad(u(x)), dS) -
integrate(lambda x: 2.0 * exp(u(x)), dV) - integrate(rhs, dV))
def apply(self, u):
def rhs(x):
z = pi / 2 * (x[0]**2 + x[1]**2)
return 2 * pi * (sin(z) + z * cos(z)) + cos(z)
return (integrate(lambda x: -n_dot_grad(u(x)), dS) +
integrate(lambda x: u(x), dV) - integrate(rhs, dV))
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
- integrate(lambda x: 2.0 * exp(u(x)), dV)
- integrate(lambda x: 2 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1]), dV)
+ integrate(lambda x: 2.0 * exp(sin(pi * x[0]) * sin(pi * x[1])), dV)
)
def apply(self, u):
def rhs(x):
return (3 * pi**2 + 1) * sin(pi * x[0]) * sin(pi * x[1]) * sin(
pi * x[2])
return (integrate(lambda x: -n_dot_grad(u(x)), dS) +
integrate(lambda x: u(x), dV) - integrate(rhs, dV))
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS) -
integrate(lambda x: 2.0 * exp(u(x)), dV) - integrate(
lambda x: 2 * pi**2 * sin(pi * x[0]) * sin(pi * x[1]), dV) +
integrate(lambda x: 2.0 * exp(sin(pi * x[0]) * sin(pi * x[1])),
dV))
def apply(self, u):
return (integrate(lambda x: -n_dot_grad(u(x)), dS) -
integrate(lambda x: 2.0 * exp(u(x)), dV) - integrate(
lambda x: (3 * pi**2 * sin(pi * x[0]) * sin(pi * x[1]) *
sin(pi * x[2]) - 2.0 * exp(self.exact_sol(x))),
dV,
))
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
+ integrate(lambda x: u(x), dV)
- integrate(
lambda x: (2 * pi ** 2 + 1) * sin(pi * x[0]) * sin(pi * x[1]), dV
)
)
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
+ integrate(lambda x: u(x), dV)
- integrate(
lambda x: (2 * pi ** 2 + 1) * sin(pi * x[0]) * sin(pi * x[1]), dV
)
)
def apply(self, u):
def rhs(x):
return (3 * pi ** 2 + 1) * sin(pi * x[0]) * sin(pi * x[1]) * sin(pi * x[2])
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
+ integrate(lambda x: u(x), dV)
- integrate(rhs, dV)
)
def apply(self, u):
def rhs(x):
z = pi / 2 * (x[0] ** 2 + x[1] ** 2)
return 2 * pi * (sin(z) + z * cos(z)) + cos(z)
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
+ integrate(lambda x: u(x), dV)
- integrate(rhs, dV)
)
def apply(self, u):
a0 = 2
a1 = 1
a = sympy.Matrix([a0, a1, 0])
return integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x), dS) - integrate(
lambda x: 2 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1])
+ a0 * pi * cos(pi * x[0]) * sin(pi * x[1])
+ a1 * pi * sin(pi * x[0]) * cos(pi * x[1]),
dV,
)
def apply(self, u):
def rhs(x):
z = pi / 2 * (x[0] ** 2 + x[1] ** 2 + x[2] ** 2)
return 2 * pi * (1.5 * sin(z) + z * cos(z)) - 2.0 * exp(cos(z))
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
- integrate(lambda x: 2.0 * exp(u(x)), dV)
- integrate(rhs, dV)
)
def apply(self, u):
a0 = 2
a1 = 1
a = sympy.Matrix([a0, a1, 0])
return integrate(
lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x), dS) - integrate(
lambda x: 2 * pi**2 * sin(pi * x[0]) * sin(pi * x[1]) + a0 * pi
* cos(pi * x[0]) * sin(pi * x[1]) + a1 * pi * sin(pi * x[
0]) * cos(pi * x[1]),
dV,
)
def apply(self, u):
def neumann(x):
z = x[0]**2 + x[1]**2
return -pi * sqrt(z) * sin(pi / 2 * z)
def rhs(x):
z = pi / 2 * (x[0]**2 + x[1]**2)
return 2 * pi * (sin(z) + z * cos(z))
return (integrate(lambda x: -n_dot_grad(u(x)), dS) -
integrate(neumann, dGamma) - integrate(rhs, dV))
def apply(self, u):
a0 = 2
a1 = 1
a = numpy.array([a0, a1, 0])
def rhs(x):
z = pi / 2 * (x[0]**2 + x[1]**2)
return (2 * pi * (sin(z) + z * cos(z)) - a0 * pi * x[0] * sin(z) -
a1 * pi * x[1] * sin(z))
return integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x),
dS) - integrate(rhs, dV)
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
- integrate(lambda x: 2.0 * exp(u(x)), dV)
- integrate(
lambda x: (
3 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1]) * sin(pi * x[2])
- 2.0 * exp(self.exact_sol(x))
),
dV,
)
)
def apply(self, u):
a0 = 2
a1 = 1
a2 = 3
a = Matrix([a0, a1, a2])
def rhs(x):
z = pi / 2 * (x[0]**2 + x[1]**2 + x[2]**2)
return (+2 * pi * (1.5 * sin(z) + z * cos(z)) -
a0 * pi * x[0] * sin(z) - a1 * pi * x[1] * sin(z) -
a2 * pi * x[2] * sin(z))
out = integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x),
dS) - integrate(rhs, dV)
return out
def apply(self, u):
a0 = 2
a1 = 1
a = numpy.array([a0, a1, 0])
def rhs(x):
z = pi / 2 * (x[0] ** 2 + x[1] ** 2)
return (
2 * pi * (sin(z) + z * cos(z))
- a0 * pi * x[0] * sin(z)
- a1 * pi * x[1] * sin(z)
)
return integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x), dS) - integrate(
rhs, dV
)
def apply(self, u):
a0 = 2
a1 = 1
a2 = 3
a = Matrix([a0, a1, a2])
def rhs(x):
z = pi / 2 * (x[0] ** 2 + x[1] ** 2 + x[2] ** 2)
return (
+2 * pi * (1.5 * sin(z) + z * cos(z))
- a0 * pi * x[0] * sin(z)
- a1 * pi * x[1] * sin(z)
- a2 * pi * x[2] * sin(z)
)
out = integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x), dS) - integrate(
rhs, dV
)
return out
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 3 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1]) * sin(pi * x[2]), dV
)
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 3 * pi**2 * sin(pi * x[0]) * sin(pi * x[1]) * sin(pi * x[
2]), dV)
def apply(self, u):
a = numpy.array([2, 1, 0])
return integrate(lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x),
dS) - integrate(lambda x: 1.0, dV)
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 2.0 * exp(u(x)), dV)
def apply(self, u):
return (integrate(lambda x: -n_dot_grad(u(x)), dS) +
integrate(lambda x: 3.0, dGamma) -
integrate(lambda x: 1.0, dV))
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 2.0 * exp(u(x)), dV
)
def apply(self, u):
return (integrate(lambda x: -1.0e-2 * n_dot_grad(u(x)), dS) +
integrate(u, dV) - integrate(lambda x: 1.0, dV))
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
- integrate(lambda x: -pi * sin(pi * x[0]), dGamma)
- integrate(lambda x: 2 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1]), dV)
)
def apply(self, u):
return (
integrate(lambda x: -1.0e-2 * n_dot_grad(u(x)), dS)
+ integrate(u, dV)
- integrate(lambda x: 1.0, dV)
)
def apply(self, u):
return integrate(lambda x: n_dot_grad(u(x)), dS)
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 50 * sin(2 * pi * x[0]), dV
)
def apply(self, u):
a = numpy.array([2, 1, 0])
return integrate(
lambda x: -n_dot_grad(u(x)) + n_dot(a) * u(x), dS
) - integrate(lambda x: 1.0, dV)
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 50 * sin(2 * pi * x[0]), dV)
def apply(self, u):
return (
integrate(lambda x: -n_dot_grad(u(x)), dS)
+ integrate(lambda x: 3.0, dGamma)
- integrate(lambda x: 1.0, dV)
)
