def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 41
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-2
minField = 1e-10
abscissa_0 = [
Expression('0.6*floor(x[0]+0.5) + 0.4*(1.0-floor(x[0]+0.5))'),
Expression('0.4*floor(x[0]+0.5) + 0.2*(1.0-floor(x[0]+0.5))')
]
weight_0 = [
Expression('0.25*floor(x[0]+0.5) + 0.25*(1.0-floor(x[0]+0.5))'),
Expression('0.25*floor(x[0]+0.5) + 0.25*(1.0-floor(x[0]+0.5))')
]
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0,
'results_6_new')
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 21
N = 2
A_cond = 1e-11
A_pert = 5e-3
D_x = 1e-3
minField = 1e-8
abscissa_0 = [
Expression('1.0+(floor(x[0]+0.5)+floor(x[1]+0.5))*1.0'),
Expression('0.5+(floor(x[0]+0.5)+floor(x[1]+0.5))*0.5')
]
weight_0 = [
Expression('minField+1.0*(floor(x[0]+0.5)+floor(x[1]+0.5))',
minField=minField),
Expression('minField+1.0*(floor(x[0]+0.5)+floor(x[1]+0.5))',
minField=minField)
]
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0,
'results_10')
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 20
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-3
G = 1.0
minField = 1e-8
abscissa_0 = [Expression("0.8", minField=minField), Expression("1.2", minField=minField)]
weight_0 = [
Expression("0.5*floor(x[0]+0.5)" + "+ minField", minField=minField),
Expression("0.5*floor(x[0]+0.5)" + "+ minField", minField=minField),
]
# Create files for storing solution
files_a = [File("results_3/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results_3/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [File("results_3/weighted_abscissa_" + str(i) + ".pvd") for i in range(N)]
files_d = [File("results_3/density.pvd"), File("results_3/mean.pvd"), File("results_3/std_dev.pvd")]
files = files_a + files_b + files_c + files_d
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0, files)
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 20
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-3
G = 1.0
minField = 1e-8
abscissa_0 = [Expression('0.8', minField=minField),
Expression('1.2', minField=minField)]
weight_0 = [Expression('0.5*floor(x[0]+0.5)' +
'+ minField', minField=minField),
Expression('0.5*floor(x[0]+0.5)' +
'+ minField', minField=minField)]
# Create files for storing solution
files_a = [File("results_3/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results_3/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [File("results_3/weighted_abscissa_" + str(i) + ".pvd") for i in range(N)]
files_d = [File("results_3/density.pvd"),
File("results_3/mean.pvd"),
File("results_3/std_dev.pvd")]
files = files_a + files_b + files_c + files_d
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0, files)
def main():
# some constants
T = 5.0
dt = 0.1
dim = 1
n_ele = 41
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-3
G = 1.0
minField = 1e-10
abscissa_0 = [
Expression("0.6*floor(x[0]+0.5) + 0.4*(1.0-floor(x[0]+0.5))"),
Expression("0.4*floor(x[0]+0.5) + 0.2*(1.0-floor(x[0]+0.5))"),
]
weight_0 = [
Expression("0.25*floor(x[0]+0.5) + 0.25*(1.0-floor(x[0]+0.5))"),
Expression("0.25*floor(x[0]+0.5) + 0.25*(1.0-floor(x[0]+0.5))"),
]
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0)
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 40
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-3
G = 1.0
minField = 1e-10
abscissa_0 = [
Expression('1.2*floor(x[0]+0.45)' + '+ 1.0*(1-ceil(x[0]-0.45))'),
Expression('1.0*floor(x[0]+0.45)' + '+ 0.8*(1-ceil(x[0]-0.45))')
]
weight_0 = [
Expression('0.45*floor(x[0]+0.45)' + '+ 0.45*(1-ceil(x[0]-0.45))' +
'+ minField',
minField=minField),
Expression('0.55*floor(x[0]+0.45)' + '+ 0.55*(1-ceil(x[0]-0.45))' +
'+ minField',
minField=minField)
]
# Create files for storing solution
files_a = [File("results_4/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results_4/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [
File("results_4/weighted_abscissa_" + str(i) + ".pvd")
for i in range(N)
]
files_d = [File("results_4/weight_S_" + str(i) + ".pvd") for i in range(N)]
files_e = [
File("results_4/weighted_abscissa_S_" + str(i) + ".pvd")
for i in range(N)
]
files_f = [
File("results_4/density.pvd"),
File("results_4/mean.pvd"),
File("results_4/std_dev.pvd"),
File("results_4/skew.pvd")
]
files = files_a + files_b + files_c + files_d + files_e + files_f
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0,
files)
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 21
N = 2
A_cond = 1e-11
A_pert = 5e-3
D_x = 1e-3
minField = 1e-8
abscissa_0 = [Expression('1.0+(floor(x[0]+0.5)+floor(x[1]+0.5))*1.0'),
Expression('0.5+(floor(x[0]+0.5)+floor(x[1]+0.5))*0.5')]
weight_0 = [Expression('minField+1.0*(floor(x[0]+0.5)+floor(x[1]+0.5))', minField=minField),
Expression('minField+1.0*(floor(x[0]+0.5)+floor(x[1]+0.5))', minField=minField)]
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0, 'results_10')
def main():
# some constants
T = 5.0
dt = 0.1
dim = 2
n_ele = 40
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-3
G = 1.0
minField = 1e-10
abscissa_0 = [
Expression("1.2*floor(x[0]+0.45)" + "+ 1.0*(1-ceil(x[0]-0.45))"),
Expression("1.0*floor(x[0]+0.45)" + "+ 0.8*(1-ceil(x[0]-0.45))"),
]
weight_0 = [
Expression("0.45*floor(x[0]+0.45)" + "+ 0.45*(1-ceil(x[0]-0.45))" + "+ minField", minField=minField),
Expression("0.55*floor(x[0]+0.45)" + "+ 0.55*(1-ceil(x[0]-0.45))" + "+ minField", minField=minField),
]
# Create files for storing solution
files_a = [File("results_4/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results_4/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [File("results_4/weighted_abscissa_" + str(i) + ".pvd") for i in range(N)]
files_d = [File("results_4/weight_S_" + str(i) + ".pvd") for i in range(N)]
files_e = [File("results_4/weighted_abscissa_S_" + str(i) + ".pvd") for i in range(N)]
files_f = [
File("results_4/density.pvd"),
File("results_4/mean.pvd"),
File("results_4/std_dev.pvd"),
File("results_4/skew.pvd"),
]
files = files_a + files_b + files_c + files_d + files_e + files_f
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0, files)
#! /usr/bin/env python
from dolfin import *
from numpy import *
import distribution_diffusion as mod
# some constants
T = 100.0
dt = 0.1
dim = 1
n_ele = 5
N = 2
A_cond = 1e-8
A_pert = 5e-3
G = 1.0
D_x = 1e-7
weighted_abscissa_0 = [Expression('1.0', G=G),Expression('1.0', G=G)]
weight_0 = [Expression('0.5'),Expression('0.5')]
# Create files for storing solution
files_a = [File("results/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [File("results/density.pvd"),
File("results/mean.pvd"),
File("results/std_dev.pvd"),
files = files_a + files_b + files_c
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, weighted_abscissa_0, weight_0, files)
def main():
# some constants
T = 1.0
dt = 0.1
dim = 1
n_ele = 10
N = 2
A_cond = 1e-11
A_pert = 5e-4
D_x = 1e-4
G = 10.0
minField = 1e-10
abscissa_0 = [Expression('G*x[0]', G=G),
Expression('G*x[0]-1.0', G=G)]
weight_0 = [Expression('0.5'),
Expression('0.5')]
# Create files for storing solution
files_a = [File("results_5/weight_" + str(i) + ".pvd") for i in range(N)]
files_b = [File("results_5/abscissa_" + str(i) + ".pvd") for i in range(N)]
files_c = [File("results_5/weighted_abscissa_" + str(i) + ".pvd") for i in range(N)]
files_d = [File("results_5/density.pvd"),File("results_5/mean.pvd"),File("results_5/std_dev.pvd")]
files_e = [File("results_5/t_density.pvd"),File("results_5/t_mean.pvd"),File("results_5/t_std_dev.pvd")]
files = files_a + files_b + files_c + files_d + files_e
# import pdb; pdb.set_trace()
mod.main(T, dt, dim, n_ele, N, A_cond, A_pert, D_x, abscissa_0, weight_0, files[:-3])
def calculateTheoryStats():
theoretical_moments = zeros([mesh.num_vertices(),2*N])
for i in range(2*N):
for j in range(N):
theoretical_moments[:,i] += 0.5 * (G*mesh.coordinates()[:,0] - 1.0*j +
sin(3**j*pi/2) *
sqrt(2*D_x.vector().array()[:]*G**2*t))**i
TheoryDensity = Function(FS)
TheoryMean = Function(FS)
TheoryStd = Function(FS)
TheoryDensity.vector()[:] = array(theoretical_moments[:,0])
TheoryMean.vector()[:] = array(theoretical_moments[:,1]/theoretical_moments[:,0])
var = (theoretical_moments[:,2]/theoretical_moments[:,0]
- (theoretical_moments[:,1]/theoretical_moments[:,0])**2)
var[var<0.0] = 0.0
TheoryStd.vector()[:] = array(sqrt(var))
files[-3] << TheoryDensity
files[-2] << TheoryMean
files[-1] << TheoryStd
# Create mesh and define function space
if dim == 1:
mesh = UnitInterval(n_ele)
if dim == 2:
mesh = UnitSquare(n_ele, n_ele)
if dim ==3:
mesh = UnitCube(n_ele, n_ele, n_ele)
FS = FunctionSpace(mesh, 'Lagrange', 1)
D_x = project(Expression('D_x', D_x=D_x), FS)
t = 0
# Time step loop for theory
while t <= T:
calculateTheoryStats()
t += dt
