Hello, I have a question
Do Fenics’s meshes within the AdaptiveNonlinearVariationalSolver can handle meshes that have periodic boundary conditions using CG-FE?
Here is a min working example of my question adapted from the auto adaptive poisson example without periodic it runs line 34, with periodic it does not line 33. Thanks for any help…
1. from dolfin import *
2. # Form compiler options
3. parameters["form_compiler"]["optimize"] = True
4. parameters["form_compiler"]["cpp_optimize"] = True
5. # Create mesh and define function space
6. mesh = UnitSquareMesh(8, 8)
7. class left(SubDomain):
8. def inside(self, x, on_boundary):
9. return x[0] < DOLFIN_EPS
10. class right(SubDomain):
11. def inside(self, x, on_boundary):
12. return x[0] > (1.0 - DOLFIN_EPS)
13. class bottom(SubDomain):
14. def inside(self, x, on_boundary):
15. return x[1] < DOLFIN_EPS
16. class top(SubDomain):
17. def inside(self, x, on_boundary):
18. return x[1] > 1.0 - DOLFIN_EPS
19. left = left()
20. right = right()
21. top = top()
22. bottom = bottom()
23. class PeriodicBoundary(SubDomain):
24. # Left boundary is "target domain" G
25. def inside(self, x, on_boundary):
26. return bool(x[0] < DOLFIN_EPS and x[0] > -DOLFIN_EPS and on_boundary)
27. # Map right boundary (H) to left boundary (G)
28. def map(self, x, y):
29. y[0] = x[0] - 1.0
30. y[1] = x[1]
31. # Define function space for system of concentrations
32. P = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
33. #V = FunctionSpace(mesh, P, constrained_domain=PeriodicBoundary()) #This implements periodic let and right and gives error
34. V = FunctionSpace(mesh, P) #This implements Neumann left and right and works
35. # Define boundary condition
36. u0 = Function(V)
37. u1 = Function(V)
38. u0 = Constant(1)
39. u1 = Constant(0)
40. bc0 = DirichletBC(V,u0, top)
41. bc1 = DirichletBC(V,u1, bottom)
42. bc = [bc0, bc1]
43. # Define variational problem
44. # Define function for the solution
45. u = Function(V)
46. v = TestFunction(V)
47. f = Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)",
48. degree=1)
49. a = inner(grad(u), grad(v))*dx()
50. L = (1.0 - 0.5/(u + 0.5))*v*dx() #made it nonlinear here...
51. F = a-L
52. # Define goal functional (quantity of interest)
53. M = u*dx()
54. # Define error tolerance
55. tol = 1.e-9
56. ###### AdaptiveNonlinearVariationalSolver ########
57. du = TrialFunction(V)
58. J = derivative(F, u, du)
59. # Solve equation F = 0 with respect to u and the given boundary
60. # conditions, such that the estimated error (measured in M) is less
61. # than tol
62. problem = NonlinearVariationalProblem(F, u, bc, J)
63. solver = AdaptiveNonlinearVariationalSolver(problem, M)
64. solver.parameters["error_control"]["dual_variational_solver"]["linear_solver"] = "default"
65. parameters["refinement_algorithm"] = "plaza_with_parent_facets"
66. solver.solve(tol)
67. solver.summary()
68. ######
69. # Output file
70. soln_init_mesh = File("init_u.pvd", "compressed")
71. soln_final_mesh = File("refined_u.pvd", "compressed")
72. soln_init_mesh << u.root_node()
73. soln_final_mesh << u.leaf_node()
the error I am getting when periodic are used is:
*** -------------------------------------------------------------------------
*** 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 check whether point is inside subdomain.
*** Reason: Function inside() not implemented by user.
*** Where: This error was encountered inside SubDomain.cpp.
*** Process: 0
***
*** DOLFIN version: 2019.1.0
*** Git changeset: 74d7efe1e84d65e9433fd96c50f1d278fa3e3f3f
*** -------------------------------------------------------------------------