Python heat_solver Examples

Example #1

File: convergence.py Project: jedman/numerics

import heat_solver
import matplotlib.pyplot as plt 
import numpy as np 
from scipy import interpolate

### gamma = 1/6 mesh refinement 
hinv = 10 
kinv = 600 
time600 = np.linspace(0,1,num=kinv+1) 
u_600 = heat_solver.heat_solver(hinv,kinv) 
gamma = hinv**2./kinv
print gamma 

hinv = 20
kinv = 2400
time2400 = np.linspace(0,1,num=kinv+1) 
u_2400 = heat_solver.heat_solver(hinv,kinv) 
gamma = hinv**2./kinv
print gamma 

hinv = 40
kinv = 9600
time9600 = np.linspace(0,1,num=kinv+1) 
u_9600 = heat_solver.heat_solver(hinv,kinv) 
gamma = hinv**2./kinv
print gamma 

x = np.linspace(0,1,num=11) 
x21 = np.linspace(0,1,num = 21) 
u_24 = interpolate.interp1d(x21,u_2400[1,:])
x41 = np.linspace(0,1,num=41) 

Example #2

File: part1.py Project: jedman/numerics

import heat_solver 
import matplotlib.pyplot as plt 
import numpy as np 
u1 = heat_solver.heat_solver(10,10) 
u2 = heat_solver.heat_solver(10,200)
u3 = heat_solver.heat_solver(10,600)
u4 = heat_solver.heat_solver(10,2000)
#u1_arc = heat_solver.heat_solver(10,600, init ='arc') 
#u_full = heat_solver.heat_solver_full(10,200)

x = np.linspace(0,1,num=11)
fig1 = plt.figure() 
ax1 = fig1.add_subplot(111)
ax1.plot(x,u1[1,:]) 
ax1.set_title('u at t=1 with $\lambda =10$')
ax1.set_xlabel('x')
ax1.set_ylabel('u')
plt.savefig('u1.pdf', bbox_inches=0)

Example #3

File: timing.py Project: jedman/numerics

import pstats, cProfile
import numpy as np
import matplotlib.pyplot as plt 
import pyximport
pyximport.install()
import heat_solver 


hinv =10 
kinv = 600
x =np.linspace(0,1,num = hinv+1)

u_sine = heat_solver.heat_solver(hinv,kinv) 
u_sine_200 = heat_solver.heat_solver(hinv, 200) 
u_arc = heat_solver.heat_solver(hinv,kinv, init ='arc')
u_arc_200 = heat_solver.heat_solver(hinv,200, init ='arc')

fig2 = plt.figure()
ax2 = fig2.add_subplot(111)  
ax2.plot(x,u_sine[1,:], label = 'numerical, $\lambda=1/6$', ls ='--', marker = 'o')
ax2.plot(x,heat_solver.exact(x,1), label = 'exact')
ax2.plot(x,u_sine_200[1,:], label = 'numerical, $\lambda=1/2$', ls ='--', marker ='x')
ax2.set_title('Exact and numerical solutions at t=1 with I.C. $\sin(\pi x)$ ')
ax2.set_xlabel('x')
ax2.set_ylabel('u')
ax2.legend()
plt.savefig('u_sine.pdf', bbox_inches=0)

fig2 = plt.figure()
ax2 = fig2.add_subplot(111)  
ax2.plot(x,u_arc[1,:], label = 'numerical,$\lambda=1/6$', ls ='--', marker ='o')