#! /usr/bin/env python
#
from fenics import *

def mitchell11 ( ):

#*****************************************************************************80
#
## mitchell11 sets up Mitchell test #11.
#
#  Discussion:
#
#    Intersecting interfaces
#    -del p del(u) = f on [-1,+1]x[-1,+1], where p is a piecewise constant function.
#    u = g on the boundary.
#
#    f = -del p del g
#    g = r^alpha1 * mu(theta)
#
#    Suggested parameter values:
#      phi = pi/2
#      p1 = R
#      p2 = 1
#      p3 = R
#      p4 = 1 
#      a1 = 0.1
#      R = 161.4476387975881
#      alpha1 = pi/4
#      beta1 = -14.92256510455152.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 August 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    William Mitchell,
#    A collection of 2D elliptic problems for testing adaptive
#    grid refinement algorithms,
#    Applied Mathematics and Computation,
#    Volume 220, 1 September 2013, pages 350-364.
#
  import matplotlib.pyplot as plt
#
#  Set parameters.
#
  theta = pi / 2
  r = 161.4476387975881
  alpha1 = pi / 4
  beta1 = -14.92256510455152
  p1 = r
  p2 = 1.0
  p3 = r
  p4 = 1.0
  a1 = 0.1
#
#  Define a mesh of triangles on [-1,+1]x[-1,+1]
#
  mesh = RectangleMesh ( -1.0, -1.0, +1.0, +1.0, 4, 4 )
#
#  Plot the mesh.
#
  plot ( mesh, title = 'Mitchell Test 11 Mesh' )
  filename = 'mitchell11_mesh.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.close ( )
#
#  Define the function space.
#
  V = FunctionSpace ( mesh, "Lagrange", 1 )
#
#  Define the exact solution.
#
  u0 = Expression ( "?" )
#
#  Apply the boundary condition to points which are on the boundary of the mesh.
#
  def u0_boundary ( x, on_boundary ):
    return on_boundary
#
#  The value to be used at Dirichlet boundary points is U0.
#
  bc = DirichletBC ( V, u0, u0_boundary )
#
#  Define the variational problem.
#
  u = TrialFunction ( V )
  v = TestFunction ( V )
  f = Expression ( "?" )
  a = inner ( nabla_grad ( u ), nabla_grad ( v ) ) * dx
  L = f * v * dx
#
#  Compute the solution.
#
  u = Function ( V )
  solve ( a == L, u, bc )
#
#  Plot the solution.
#
  plot ( u )

  return

def mitchell11_test ( ):

#*****************************************************************************80
#
## mitchell11_test tests mitchell11.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 October 2018
#
#  Author:
#
#    John Burkardt
#

#
#  Report level = only warnings or higher.
#
  level = 30
  set_log_level ( level )

  print ( '' )
  print ( 'mitchell11_test:' )
  print ( '  FENICS/Python version' )
  print ( '  Mitchell test problem #11.' )

  mitchell11 ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'mitchell11_test:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):

  mitchell11_test ( )