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
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
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
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