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

def mitchell10 ( ):

#*****************************************************************************80
#
## mitchell10 sets up Mitchell test #10.
#
#  Interior line singularity
#  -Laplace(u) = f on [-1,+1]x[-1,+1]
#  u = u0 on the boundary.
#  u0 = cos(pi*y/2)                        for x <= beta*(y+1)
#     = cos(pi*y/2)+(x-beta*(y+1))**alpha  for      beta*(y+1) < x
#  f = -Laplace(u).
#
#  Discussion:
#
#    Suggested parameter values:
#    * alpha = 2.5, beta = 0.0
#    * alpha = 1.1, beta = 0.0
#    * alpha = 1.5, beta = 0.6
#
#  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.
#
  alpha = 2.5
  beta = 0.0
#
#  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 10 Mesh' )
  filename = 'mitchell10_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 mitchell10_test ( ):

#*****************************************************************************80
#
## mitchell10_test tests mitchell10.
#
#  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 ( 'mitchell10_test:' )
  print ( '  FENICS/Python version' )
  print ( '  Mitchell test problem #10.' )

  mitchell10 ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'mitchell10_test:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):

  mitchell10_test ( )