FiPy script to test time scaling with dimension

solverscaling.py

from fipy import *
import time

# Spatial parameters
nx = 27000 # bins
dx = 1. 
L = nx * dx

# Diffusion and time step
D = 1.
dt = 10. * dx**2 / (2 * D)
steps = 10

# radius of nucleus
r = 3.0

mesh = Grid1D(nx=nx, dx=dx)
X = mesh.cellCenters[0]  # These are large arrays
phi = CellVariable(mesh=mesh, name=r"$\phi$", value=0., hasOld=True)

eq = TransientTerm() == DiffusionTerm(coeff=D) 

# Initial concentration is a segment located in the center of a bounded line
phi.setValue(1.0, where=( ((X-L/2)**2) < r**2) )

# Solve

print "1D"
print

start_time = time.time()
last_time = start_time
for step in range(steps):
    phi.updateOld()
    eq.solve(var=phi, dt=dt)
    print step, 'elapsed:', time.time() - last_time
    last_time = time.time()
print 'Total time elapsed:', time.time() - start_time

print


# Spatial parameters
nx = ny = 164 # bins
dx = dy = 1.  
L = nx * dx

mesh = Grid2D(nx=nx, ny=ny, dx=dx, dy=dy)
X, Y = mesh.cellCenters  # These are large arrays
phi = CellVariable(mesh=mesh, name=r"$\phi$", value=0., hasOld=True)

eq = TransientTerm() == DiffusionTerm(coeff=D) 

# Initial concentration is a circle located in the center of a bounded square
phi.setValue(1.0, where=( ((X-L/2)**2 + (Y-L/2)**2) < r**2) )

# Solve

print "2D"
print

start_time = time.time()
last_time = start_time
for step in range(steps):
    phi.updateOld()
    eq.solve(var=phi, dt=dt)
    print step, 'elapsed:', time.time() - last_time
    last_time = time.time()
print 'Total time elapsed:', time.time() - start_time

print

# Spatial parameters
nx = ny = nz = 30 # bins
dx = dy = dz = 1. 
L = nx * dx

# radius of nucleus
r = 3.0

mesh = Grid3D(nx=nx, ny=ny, nz=nz, dx=dx, dy=dy, dz=dz)
X, Y, Z = mesh.cellCenters  # These are large arrays
phi = CellVariable(mesh=mesh, name=r"$\phi$", value=0., hasOld=True)

eq = TransientTerm() == DiffusionTerm(coeff=D) 

# Initial concentration is a sphere located in the center of a bounded cube
phi.setValue(1.0, where=( ((X-L/2)**2 + (Y-L/2)**2 + (Z-L/2)**2) < r**2) )

# Solve

print "3D"
print

start_time = time.time()
last_time = start_time
for step in range(steps):
    phi.updateOld()
    eq.solve(var=phi, dt=dt)
    print step, 'elapsed:', time.time() - last_time
    last_time = time.time()
print 'Total time elapsed:', time.time() - start_time