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: 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 + 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): 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): 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 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: 3.0, dGamma) - integrate(lambda x: 1.0, 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)) return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(rhs, 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): 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: 3 * pi ** 2 * sin(pi * x[0]) * sin(pi * x[1]) * sin(pi * x[2]), 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: 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: 2.0 * exp(u(x)), 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)
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: 2 * pi**2 * 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: 3.0, dGamma) - integrate(lambda x: 1.0, dV) )