def solve(self, **arguments):
t_start = time.clock()
# definig Function space on this mesh using Lagrange
#polynoimals of degree 1.
H = FunctionSpace(self.mesh, "CG", 1)
# Setting up the variational problem
v = TrialFunction(H)
w = TestFunction(H)
coeff_dx2 = Constant(1)
coeff_v = Constant(1)
f = Expression("(4*pow(pi,2))*exp(-(1/coeff_v)*t)*sin(2*pi*x[0])",
{'coeff_v': coeff_v},
degree=2)
v0 = Expression("sin(2*pi*x[0])", degree=2)
f.t = 0
def boundary(x, on_boundary):
return on_boundary
bc = DirichletBC(H, v0, boundary)
v1 = interpolate(v0, H)
dt = self.steps.time
a = (dt * inner(grad(v), grad(w)) + dt * coeff_v * inner(v, w)) * dx
L = (f * dt - coeff_v * v1) * w * dx
A = assemble(a)
v = Function(H)
T = self.domain.time[-1]
t = dt
# solving the variational problem.
while t <= T:
b = assemble(L, tensor=b)
vo.t = t
bc.apply(A, b)
solve(A, v.vector(), b)
t += dt
v1.assign(v)
self.solution.extend(v.vector().array())
return [self.solution, time.clock() - t_start]
def solve(self, **arguments):
t_start = time.clock()
# definig Function space on this mesh using Lagrange
#polynoimals of degree 1.
H = FunctionSpace(self.mesh, "CG", 1)
# Setting up the variational problem
v = TrialFunction(H)
w = TestFunction(H)
epsilon = Constant(arguments[Components().Diffusion])
f = Expression("(1 - epsilon*4*pow(pi,2))*cos(2*pi*x[0])",\
epsilon=epsilon, degree=1)
a = (epsilon * inner(grad(v), grad(w)) + inner(v, w)) * dx
L = f * w * dx
# solving the variational problem.
v = Function(H)
solve(a == L, v)
self.solution.extend(v.vector().array())
return [self.solution, time.clock() - t_start]
def solve(self, **arguments):
t_start = time.clock()
# definig Function space on this mesh using Lagrange
#polynoimals of degree 1.
H = FunctionSpace(self.mesh, "CG", 1)
# Setting up the variational problem
v = TrialFunction(H)
w = TestFunction(H)
epsilon = Constant(arguments[Components().Diffusion])
f = Constant(0)
a = (epsilon * inner(grad(v), grad(w)) + inner(v, w)) * dx
#Still have to figure it how to use a Neumann Condition here
L = f * w * dx
# solving the variational problem.
v = Function(H)
solve(a == L, v)
self.solution.extend(v.vector().array())
return [self.solution, time.clock() - t_start]