def fd1d_heat_explicit_test02 ( ):

#*****************************************************************************80
#
## FD1D_HEAT_EXPLICIT_TEST02 does a problem with known solution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    06 November 2014
#
#  Author:
#
#    John Burkardt
#
  from fd1d_heat_explicit import fd1d_heat_explicit
  from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
  from math import sqrt
  from r8mat_write import r8mat_write
  from r8vec_write import r8vec_write
  from mpl_toolkits.mplot3d import Axes3D
  from matplotlib import cm
  from matplotlib.ticker import LinearLocator, FormatStrFormatter
  import matplotlib.pyplot as plt
  import numpy as np

  print ''
  print 'FD1D_HEAT_EXPLICIT_TEST02:'
  print '  Compute an approximate solution to the time-dependent'
  print '  one dimensional heat equation for a problem where we'
  print '  know the exact solution.'
  print ''
  print '    dH/dt - K * d2H/dx2 = f(x,t)'
  print ''
  print '  Run a simple test case.'
#
#  Heat coefficient.
#
  k = k_test02 ( )
#
#  X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
  x_num = 21
  x_min = 0.0
  x_max = 1.0
  dx = ( x_max - x_min ) / ( x_num - 1 )
  x = np.linspace ( x_min, x_max, x_num )
#
#  T_NUM is the number of equally spaced time points between 0 and 10.0.
#
  t_num = 26
  t_min = 0.0
  t_max = 10.0
  dt = ( t_max - t_min ) / ( t_num - 1 )
  t = np.linspace ( t_min, t_max, t_num )
#
#  Get the CFL coefficient.
#
  cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )

  print ''
  print '  Number of X nodes = %d' % ( x_num )
  print '  X interval is [%f,%f]' % ( x_min, x_max )
  print '  X spacing is %f' % ( dx )
  print '  Number of T values = %d' % ( t_num )
  print '  T interval is [%f,%f]' % ( t_min, t_max )
  print '  T spacing is %f' % ( dt )
  print '  Constant K = %g' % ( k )
  print '  CFL coefficient = %g' % ( cfl )
#
#  Running the code produces an array H of temperatures H(t,x),
#  and vectors x and t.
#
  gmat = np.zeros ( ( x_num, t_num ) )
  hmat = np.zeros ( ( x_num, t_num ) )

  print ''
  print '  Step            Time       RMS Error'
  print ''

  for j in range ( 0, t_num ):

    if ( j == 0 ):
      h = ic_test02 ( x_num, x, t[j] )
      h = bc_test02 ( x_num, x, t[j], h )
    else:
      h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test02, bc_test02, h )

    g = exact_test02 ( x_num, x, t[j] )

    e = 0.0
    for i in range ( 0, x_num ):
      e = e + ( h[i] - g[i] ) ** 2
    e = sqrt ( e ) / sqrt ( x_num )

    print '  %4d  %14.6g  %14.6g' % ( j, t[j], e )
    for i in range ( 0, x_num ):
      gmat[i,j] = g[i]
      hmat[i,j] = h[i]
#
#  Plot the data.
#
  tmat, xmat = np.meshgrid ( t, x )
  fig = plt.figure ( )
  ax = Axes3D ( fig )
  surf = ax.plot_surface ( xmat, tmat, hmat )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---T--->' )
  plt.title ( 'U(X,T)' )
  plt.savefig ( 'plot_test02.png' )
  plt.show ( )
#
#  Write the data to files.
#
  r8mat_write ( 'g_test02.txt', x_num, t_num, gmat )
  r8mat_write ( 'h_test02.txt', x_num, t_num, hmat )
  r8vec_write ( 't_test02.txt', t_num, t )
  r8vec_write ( 'x_test02.txt', x_num, x )

  print ''
  print '  G(X,T) written to "g_test02.txt"'
  print '  H(X,T) written to "h_test02.txt"'
  print '  T values written to "t_test02.txt"'
  print '  X values written to "x_test02.txt"'

  return
예제 #2
0
def fd1d_heat_explicit_test03():

    #*****************************************************************************80
    #
    ## FD1D_HEAT_EXPLICIT_TEST03 does a simple test problem.
    #
    #  Licensing:
    #
    #    This code is distributed under the GNU LGPL license.
    #
    #  Modified:
    #
    #    06 November 2014
    #
    #  Author:
    #
    #    John Burkardt
    #
    from fd1d_heat_explicit import fd1d_heat_explicit
    from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
    from math import sqrt
    from r8mat_write import r8mat_write
    from r8vec_write import r8vec_write
    from mpl_toolkits.mplot3d import Axes3D
    from matplotlib import cm
    from matplotlib.ticker import LinearLocator, FormatStrFormatter
    import matplotlib.pyplot as plt
    import numpy as np

    print ''
    print 'FD1D_HEAT_EXPLICIT_TEST03:'
    print '  Compute an approximate solution to the time-dependent'
    print '  one dimensional heat equation:'
    print ''
    print '    dH/dt - K * d2H/dx2 = f(x,t)'
    print ''
    print '  Run a simple test case.'
    #
    #  Heat coefficient.
    #
    k = k_test03()
    #
    #  X_NUM is the number of equally spaced nodes to use between 0 and 1.
    #
    x_num = 21
    x_min = -5.0
    x_max = +5.0
    dx = (x_max - x_min) / (x_num - 1)
    x = np.linspace(x_min, x_max, x_num)
    #
    #  T_NUM is the number of equally spaced time points between 0 and 10.0.
    #
    t_num = 81
    t_min = 0.0
    t_max = 4.0
    dt = (t_max - t_min) / (t_num - 1)
    t = np.linspace(t_min, t_max, t_num)
    #
    #  Get the CFL coefficient.
    #
    cfl = fd1d_heat_explicit_cfl(k, t_num, t_min, t_max, x_num, x_min, x_max)

    print ''
    print '  Number of X nodes = %d' % (x_num)
    print '  X interval is [%f,%f]' % (x_min, x_max)
    print '  X spacing is %f' % (dx)
    print '  Number of T values = %d' % (t_num)
    print '  T interval is [%f,%f]' % (t_min, t_max)
    print '  T spacing is %f' % (dt)
    print '  Constant K = %g' % (k)
    print '  CFL coefficient = %g' % (cfl)
    #
    #  Running the code produces an array H of temperatures H(t,x),
    #  and vectors x and t.
    #
    hmat = np.zeros((x_num, t_num))

    for j in range(0, t_num):
        if (j == 0):
            h = ic_test03(x_num, x, t[j])
            h = bc_test03(x_num, x, t[j], h)
        else:
            h = fd1d_heat_explicit(x_num, x, t[j - 1], dt, cfl, rhs_test03,
                                   bc_test03, h)
        for i in range(0, x_num):
            hmat[i, j] = h[i]


#
#  Plot the data.
#
    tmat, xmat = np.meshgrid(t, x)
    fig = plt.figure()
    ax = Axes3D(fig)
    surf = ax.plot_surface(xmat, tmat, hmat)
    plt.xlabel('<---X--->')
    plt.ylabel('<---T--->')
    plt.title('U(X,T)')
    plt.savefig('plot_test03.png')
    plt.show()
    #
    #  Write the data to files.
    #
    r8mat_write('h_test03.txt', x_num, t_num, hmat)
    r8vec_write('t_test03.txt', t_num, t)
    r8vec_write('x_test03.txt', x_num, x)

    print ''
    print '  H(X,T) written to "h_test03.txt"'
    print '  T values written to "t_test03.txt"'
    print '  X values written to "x_test3.txt"'
    return
예제 #3
0
def fd1d_heat_explicit_test01(path,mode,weightsFile):
  """fd1d_heat_explicit_test01 does a simple test problem"""

  from fd1d_heat_explicit import fd1d_heat_explicit
  from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
  from r8mat_write import r8mat_write
  from r8vec_write import r8vec_write
  from mpl_toolkits.mplot3d import Axes3D
  from matplotlib import cm
  from matplotlib.ticker import LinearLocator, FormatStrFormatter
  import matplotlib.pyplot as plt
  import numpy as np

  print ''
  print 'FD1D_HEAT_EXPLICIT_TEST01:'
  print '  Compute an approximate solution to the time-dependent'
  print '  one dimensional heat equation:'
  print ''
  print '    dH/dt - K * d2H/dx2 = f(x,t)'
  print ''
  print '  Run a simple test case.'

  
  """Heat coefficient"""
 
  k = k_test01 ( )

#
#  X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
  x_num = 21
  x_min = 0.0
  x_max = 1.0
  dx = ( x_max - x_min ) / ( x_num - 1 )
  x = np.linspace ( x_min, x_max, x_num )

#
#  T_NUM is the number of equally spaced time points between 0 and 10.0.
#
  t_num = 201
  t_min = 0.0
  t_max = 80.0
  dt = ( t_max - t_min ) / ( t_num - 1 )
  t = np.linspace ( t_min, t_max, t_num )

#
#  Get the CFL coefficient.
#
  cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )

  print ''
  print '  Number of X nodes = %d' % ( x_num )
  print '  X interval is [%f,%f]' % ( x_min, x_max )
  print '  X spacing is %f' % ( dx )
  print '  Number of T values = %d' % ( t_num )
  print '  T interval is [%f,%f]' % ( t_min, t_max )
  print '  T spacing is %f' % ( dt )
  print '  Constant K = %g' % ( k )
  print '  CFL coefficient = %g' % ( cfl )
#
#  Running the code produces an array H of temperatures H(t,x),
#  and vectors x and t.
#
  hmat = np.zeros ( ( x_num, t_num ) )

  for j in range ( 0, t_num ):
    if ( j == 0 ):
      h = ic_test01 ( x_num, x, t[j] ,mode)
      h = bc_test01 ( x_num, x, t[j], h ,mode)
      
    else:
      h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test01, bc_test01, h, mode, weightsFile )
    
    for i in range ( 0, x_num ):
      hmat[i,j] = h[i]
#
#  Plot the data.
#
  tmat, xmat = np.meshgrid ( t, x )
  fig = plt.figure ( )
  ax = fig.add_subplot ( 111, projection = '3d' )
  ax = Axes3D ( fig )
  surf = ax.plot_surface ( xmat, tmat, hmat )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---T--->' )
  plt.title ( 'U(X,T)' )
  save_at  = path.strip()
  print path, save_at
  filename = str(save_at) + 'plot_test_' + str(mode)  + '.png'
  print filename
  plt.savefig (filename)
  #plt.show ( )
#
#  Write the data to files.
#
  filename = str(save_at) + 'h_test01.txt'
  r8mat_write ( filename, x_num, t_num, hmat )
  #filename = str(save_at) + 't_test01.txt'
  #r8vec_write ( filename, t_num, t )
  #filename = str(save_at) + 'x_test01.txt'
  #r8vec_write ( filename, x_num, x )

  print ''
  print '  H(X,T) written to "h_test01.txt"'
  print '  T values written to "t_test01.txt"'
  print '  X values written to "x_test01.txt"'
#
#  Terminate.
#
  print ''
  print 'FD1D_HEAT_EXPLICIT_TEST01:'
  print '  Normal end of execution.'

  return
def fd1d_heat_explicit_test01():

    # *****************************************************************************80
    #
    ## FD1D_HEAT_EXPLICIT_TEST01 does a simple test problem
    #
    #  Licensing:
    #
    #    This code is distributed under the GNU LGPL license.
    #
    #  Modified:
    #
    #    06 November 2014
    #
    #  Author:
    #
    #    John Burkardt
    #
    from fd1d_heat_explicit import fd1d_heat_explicit
    from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
    from r8mat_write import r8mat_write
    from r8vec_write import r8vec_write
    from mpl_toolkits.mplot3d import Axes3D
    from matplotlib import cm
    from matplotlib.ticker import LinearLocator, FormatStrFormatter
    import matplotlib.pyplot as plt
    import numpy as np

    print ""
    print "FD1D_HEAT_EXPLICIT_TEST01:"
    print "  Compute an approximate solution to the time-dependent"
    print "  one dimensional heat equation:"
    print ""
    print "    dH/dt - K * d2H/dx2 = f(x,t)"
    print ""
    print "  Run a simple test case."
    #
    #  Heat coefficient.
    #
    k = k_test01()
    #
    #  X_NUM is the number of equally spaced nodes to use between 0 and 1.
    #
    x_num = 21
    x_min = 0.0
    x_max = 1.0
    dx = (x_max - x_min) / (x_num - 1)
    x = np.linspace(x_min, x_max, x_num)
    #
    #  T_NUM is the number of equally spaced time points between 0 and 10.0.
    #
    t_num = 201
    t_min = 0.0
    t_max = 80.0
    dt = (t_max - t_min) / (t_num - 1)
    t = np.linspace(t_min, t_max, t_num)
    #
    #  Get the CFL coefficient.
    #
    cfl = fd1d_heat_explicit_cfl(k, t_num, t_min, t_max, x_num, x_min, x_max)

    print ""
    print "  Number of X nodes = %d" % (x_num)
    print "  X interval is [%f,%f]" % (x_min, x_max)
    print "  X spacing is %f" % (dx)
    print "  Number of T values = %d" % (t_num)
    print "  T interval is [%f,%f]" % (t_min, t_max)
    print "  T spacing is %f" % (dt)
    print "  Constant K = %g" % (k)
    print "  CFL coefficient = %g" % (cfl)
    #
    #  Running the code produces an array H of temperatures H(t,x),
    #  and vectors x and t.
    #
    hmat = np.zeros((x_num, t_num))

    for j in range(0, t_num):
        if j == 0:
            h = ic_test01(x_num, x, t[j])
            h = bc_test01(x_num, x, t[j], h)
        else:
            h = fd1d_heat_explicit(x_num, x, t[j - 1], dt, cfl, rhs_test01, bc_test01, h)
        for i in range(0, x_num):
            hmat[i, j] = h[i]
    #
    #  Plot the data.
    #
    tmat, xmat = np.meshgrid(t, x)
    fig = plt.figure()
    # ax = fig.add_subplot ( 111, projection = '3d' )
    ax = Axes3D(fig)
    surf = ax.plot_surface(xmat, tmat, hmat)
    plt.xlabel("<---X--->")
    plt.ylabel("<---T--->")
    plt.title("U(X,T)")
    plt.savefig("plot_test01.png")
    plt.show()
    #
    #  Write the data to files.
    #
    r8mat_write("h_test01.txt", x_num, t_num, hmat)
    r8vec_write("t_test01.txt", t_num, t)
    r8vec_write("x_test01.txt", x_num, x)

    print ""
    print '  H(X,T) written to "h_test01.txt"'
    print '  T values written to "t_test01.txt"'
    print '  X values written to "x_test01.txt"'
    #
    #  Terminate.
    #
    print ""
    print "FD1D_HEAT_EXPLICIT_TEST01:"
    print "  Normal end of execution."

    return
예제 #5
0
def fd1d_heat_explicit_test02 ( ):
# FD1D_HEAT_EXPLICIT_TEST03 does a simple test problem.
  from fd1d_heat_explicit import fd1d_heat_explicit
  from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
  from math import sqrt
  from r8mat_write import r8mat_write
  from r8vec_write import r8vec_write
  from mpl_toolkits.mplot3d import Axes3D
  from matplotlib import cm
  from matplotlib.ticker import LinearLocator, FormatStrFormatter
  import matplotlib.pyplot as plt
  import numpy as np

  print ''
  print 'FD1D_HEAT_EXPLICIT_TEST03:'
  print '  Compute an approximate solution to the time-dependent'
  print '  one dimensional heat equation:'
  print ''
  print '    dH/dt - K * d2H/dx2 = f(x,t)'
  print ''
  print '  Run a simple test case.'
#
#  Heat coefficient.
#
  k = k_test02 ( )
#
#  X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
  x_num = 21
  x_min = -5.0
  x_max = +5.0
  dx = ( x_max - x_min ) / ( x_num - 1 )
  x = np.linspace ( x_min, x_max, x_num )
#
#  T_NUM is the number of equally spaced time points between 0 and 10.0.
#
  t_num = 81
  t_min = 0.0
  t_max = 4.0
  dt = ( t_max - t_min ) / ( t_num - 1 )
  t = np.linspace ( t_min, t_max, t_num )
#
#  Get the CFL coefficient.
#
  cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )

  print ''
  print '  Number of X nodes = %d' % ( x_num )
  print '  X interval is [%f,%f]' % ( x_min, x_max )
  print '  X spacing is %f' % ( dx )
  print '  Number of T values = %d' % ( t_num )
  print '  T interval is [%f,%f]' % ( t_min, t_max )
  print '  T spacing is %f' % ( dt )
  print '  Constant K = %g' % ( k )
  print '  CFL coefficient = %g' % ( cfl )
#
#  Running the code produces an array H of temperatures H(t,x),
#  and vectors x and t.
#
  hmat = np.zeros ( ( x_num, t_num ) )

  for j in range ( 0, t_num ):
    if ( j == 0 ):
      h = ic_test02 ( x_num, x, t[j] )
      h = bc_test02 ( x_num, x, t[j], h )
    else:
      h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test02, bc_test02, h )
    for i in range ( 0, x_num ):
      hmat[i,j] = h[i]
#
#  Plot the data.
#
  tmat, xmat = np.meshgrid ( t, x )
  fig = plt.figure ( )
  ax = Axes3D ( fig )
  surf = ax.plot_surface ( xmat, tmat, hmat )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---T--->' )
  plt.title ( 'U(X,T)' )
  plt.savefig ( 'plot_test02.png' )
  plt.show ( )
#
#  Write the data to files.
#
  r8mat_write ( 'h_test02.txt', x_num, t_num, hmat )
  r8vec_write ( 't_test02.txt', t_num, t )
  r8vec_write ( 'x_test02.txt', x_num, x )

  print ''
  print '  H(X,T) written to "h_test02.txt"'
  print '  T values written to "t_test02.txt"'
  print '  X values written to "x_test3.txt"'
  return