Dear all,
First of all thanks for the support in all my silly questions.
I am trying to implement the code below using Newton-Raphson, but this problem has only initial guess (no boundary conditions) and I have no idea how can I do this work.
# Modules
from fenics import*
import time
%matplotlib inline
# Parameters
theta = Constant(0.5) # theta schema
t_end = 5.0
num_steps = 10
dt = t_end/num_steps
mesh = RectangleMesh(Point(0.0, 0.0), Point(1.0, 4.0), 1, 1,"crossed")
center = Point(0.5, 0.5)
radius = 0.2
dist = Expression('sqrt((x[0]-A)*(x[0]-A) + (x[1]-B)*(x[1]-B))-r',degree=2, A=center[0], B=center[1],r=radius)
# Difine function space
V = FunctionSpace(mesh, "Lagrange", 1)
u = Function(V)
u0 = Function(V)
w = TestFunction(V)
#initial condition
u0 = interpolate(dist, V)
# Reinitalization
n = grad(u0)
h = CellSize(mesh)
epsilon = 2*h
beta = theta*dt
F = u*w*dx - beta*u*inner(grad(w),n)*dx + epsilon*beta*inner(grad(u),n)*inner(grad(w),n)*dx + \
epsilon*dt*u*u0*inner(grad(w),n)*dx - (u0*w*dx + beta*u0*inner(grad(w),n)*dx - \
epsilon*beta*inner(grad(u0),n)*inner(grad(w),n)*dx)
J = derivative(F, u)
bcs = Constant(0)
ffc_options={"quadrature_degree":4,"optimize":True,"eliminate_zeros":False}
problem=NonlinearVariationalProblem(F,u,bcs,J,ffc_options)
solver=NonlinearVariationalSolver(problem)
prm = solver.parameters
#info(prm, True)
prm['nonlinear_solver'] = 'newton'
prm['newton_solver']['linear_solver'] = 'mumps'
prm['newton_solver']['lu_solver']['report'] = False
prm['newton_solver']['lu_solver']['same_nonzero_pattern']=True
prm['newton_solver']['absolute_tolerance'] = 1E-10
prm['newton_solver']['relative_tolerance'] = 1E-10
prm['newton_solver']['maximum_iterations'] = 20
prm['newton_solver']['report'] = True
#prm['newton_solver']['error_on_nonconvergence'] = False
error:
RuntimeErrorTraceback (most recent call last)
<ipython-input-5-39e0129517f4> in <module>()
1 ffc_options={"quadrature_degree":4,"optimize":True,"eliminate_zeros":False}
----> 2 problem=NonlinearVariationalProblem(F,u,bcs,J,ffc_options)
3 solver=NonlinearVariationalSolver(problem)
4
5 prm = solver.parameters
/usr/local/lib/python2.7/dist-packages/dolfin/fem/solving.py in __init__(self, F, u, bcs, J, form_compiler_parameters)
135 # Extract and check arguments
136 u = _extract_u(u)
--> 137 bcs = _extract_bcs(bcs)
138
139 # Store input UFL forms and solution Function
/usr/local/lib/python2.7/dist-packages/dolfin/fem/solving.py in _extract_bcs(bcs)
491 cpp.dolfin_error("solving.py",
492 "solve variational problem",
--> 493 "Unable to extract boundary condition arguments")
494 return bcs
/usr/local/lib/python2.7/dist-packages/dolfin/cpp/common.py in dolfin_error(location, task, reason)
2910
2911 """
-> 2912 return _common.dolfin_error(location, task, reason)
2913
2914 def deprecation(feature, version_deprecated, message):
RuntimeError:
*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
*** fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error: Unable to solve variational problem.
*** Reason: Unable to extract boundary condition arguments.
*** Where: This error was encountered inside solving.py.
*** Process: 0
***
*** DOLFIN version: 2016.2.0
*** Git changeset: 0f003bc07ee5fd583fb956245016d5972b80fea1
