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Commit 8ab2655e by Jigyasa Watwani
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moving and renaming files

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Showing with 124 additions and 437 deletions
fem_errors.py deleted 100644 → 0
import dolfin as df
import matplotlib.pyplot as plt
import numpy as np
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
def laplace(Nx, L, cL, cR):
# mesh, function space, function, test function
mesh = df.IntervalMesh(Nx, 0, L)
x = mesh.coordinates()[:,0]
function_space = df.FunctionSpace(mesh, 'P', 1)
c, tc = df.Function(function_space), df.TestFunction(function_space)
# Dirichlet boundary
dbc = df.DirichletBC(function_space, df.Constant(0), 'on_boundary')
def left(x, on_boundary): # inhomogeneous dirichlet boundary
return df.near(x[0], 0.0) and on_boundary
def right(x, on_boundary):
return df.near(x[0], L) and on_boundary
dbc_left = df.DirichletBC(function_space, df.Constant(cL), left)
dbc_right = df.DirichletBC(function_space, df.Constant(cR), right)
dbc = [dbc_left, dbc_right]
# form
form = (-df.inner(c.dx(0), tc.dx(0)) + df.inner(tc, df.Expression('sin(x[0])', degree=1))) * df.dx(mesh)
# solve
df.solve(form == 0, c, dbc)
c_numerical = c.compute_vertex_values(mesh)
# exact solution
c_exact = np.sin(x)
# plot
# plt.plot(x, c_numerical, 'bo', label='Numerical solution')
# plt.plot(x, c_exact, label='Exact solution')
# plt.xlabel('x')
# plt.ylabel('$c(x)$')
# plt.legend()
# plt.show()
error = np.max(np.abs(c_numerical - c_exact))
return(error)
# parameters
L, cL, cR = np.pi, 0, 0
Nx_array = np.array([5, 10, 20, 40, 80, 100, 200, 400, 800, 1600])
dx_array = L/Nx_array
error_array = np.zeros(len(dx_array))
for i in range(0, len(dx_array)):
error_array[i] = laplace(Nx_array[i], L, cL, cR)
plt.loglog(dx_array, error_array, 'bo')
plt.show()
\ No newline at end of file
fixed_boundaries.json deleted 100644 → 0
{
"morphogen" : false,
"dimension" : 2,
"meshfile": "circle2.xml.gz",
"resolution" : 16,
"system_size_by_2PI" : 1 ,
"bulk_elasticity" : 0.0,
"shear_elasticity": 0.0,
"shear_viscosity" : 1.0,
"bulk_viscosity" : 1.0,
"friction" : 1.0,
"lamda": 8.5,
"diffusion_rho" : 1.0,
"turnover_rho" : 0.0,
"average_rho" : 1.0,
"saturation_rho" : 1.0,
"diffusion_c" : 0.0,
"turnover_c" : 0.0,
"average_c" : 0.0,
"noise_level": 0.1,
"timestep" : 0.01,
"savetime": 0.5,
"maxtime" : 50.0
}
fixed_domain/diffusion_fixed_domain_solution.py deleted 100644 → 0
import dolfin as df
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import progressbar
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
Nx, L, D, tmax, dt = 32, 1, 0.1, 0.25, 0.25/400
Nt = int(tmax/dt)
mesh = df.IntervalMesh(Nx, 0, L)
x = mesh.coordinates()[:, 0]
times = np.linspace(0, tmax, Nt+1)
SFS = df.FunctionSpace(mesh, 'P', 1)
c = df.Function(SFS)
tc = df.TestFunction(SFS)
c0 = df.Function(SFS)
c0.interpolate(df.Expression('1 + 0.1 * cos(2*pi*x[0]/L) + 0.2 * cos(3*pi*x[0]/L)', pi=np.pi,L=L, degree=1))
c_exact = np.zeros((Nt+1, Nx+1))
for i in range(Nt+1):
c_exact[i] = 1 + 0.1 * np.cos(2*np.pi*x/L) * np.exp(-4*np.pi**2*D*times[i]/L**2) + 0.2 * np.cos(3*np.pi*x/L) * np.exp(-9*np.pi**2*D*times[i]/L**2)
c_array = np.zeros((Nt+1, Nx+1))
c_array[0] = c0.compute_vertex_values(mesh)
cform = (df.inner((c - c0)/dt, tc)
+ D * df.inner(df.nabla_grad(c), df.nabla_grad(tc))) * df.dx
for i in progressbar.progressbar(range(1, Nt+1)):
df.solve(cform == 0, c)
c0.assign(c)
c_array[i] = c0.compute_vertex_values(mesh)
fig, (ax, ax1) = plt.subplots(2, 1)
fig.suptitle(r'$N_x = %d, \Delta t = %4.3f$' % (Nx, dt))
cplot, = ax.plot(x, c_array[0], 'ro', mfc='none', ms=6, label='Numerics')
ceplot, = ax.plot(x, c_exact[0], label='Exact')
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$c(x,t)$')
ax.legend(loc=1)
error = np.abs(c_array - c_exact)
print('Max error at t=0.25 is',np.max(error[-1]))
err_plot, = ax1.plot(x, error[1], 'bo', mfc='none', ms=6)
ax1.set_ylim(np.min(error), np.max(error))
ax1.set_xlabel(r'$x$')
ax1.set_ylabel(r'$c(x,t)-c_{\rm exact}(x,t)$')
def update(val):
ti = (abs(times-val)).argmin()
cplot.set_ydata(c_array[ti])
ceplot.set_ydata(c_exact[ti])
err_plot.set_ydata(error[ti])
plt.draw()
sax = plt.axes([0.1, 0.92, 0.7, 0.025])
sl = Slider(sax, 't', times.min(), times.max(), valinit=times.min())
sl.on_changed(update)
plt.show()
growing_domain/full_model/growing_domain.py
import dolfin as df
import numpy as np
import os
import progressbar
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
......@@ -24,6 +25,7 @@ class Growing_Domain(object):
else:
self.mesh = df.RectangleMesh(df.Point(0,0), df.Point(L,L),
self.resolution, self.resolution)
# self.mesh = df.EllipseMesh(df.Point(0.0, 0.0), [3.0, 1.0], 0.2)
scalar_element = df.FiniteElement('P', self.mesh.ufl_cell(), 1)
vector_element = df.VectorElement('P', self.mesh.ufl_cell(), 1)
......@@ -31,17 +33,14 @@ class Growing_Domain(object):
# u, v, rho, c
mixed_element = df.MixedElement([vector_element, vector_element,
scalar_element, scalar_element])
self.savedata = self.save_data_uvrhoc
else:
# u, v, rho
mixed_element = df.MixedElement([vector_element, vector_element, scalar_element])
self.savedata = self.save_data_uvrho
# define function space with this mixed element
self.function_space = df.FunctionSpace(self.mesh, mixed_element)
# dirichlet boundaries for rho
self.bc = df.DirichletBC(self.function_space.sub(2), df.Constant(0.0), 'on_boundary')
# define the reqd functions on this function space
......@@ -88,22 +87,33 @@ class Growing_Domain(object):
+ self.reaction_c(c, tc))
def setup_initial_conditions(self):
# ic for u
if self.dimension==1:
self.zero_vector = df.Constant((0.0,))
elif self.dimension==2:
self.zero_vector = df.Constant((0.0, 0.0))
u0 = df.interpolate(self.zero_vector, self.function_space.sub(0).collapse())
rho0 = df.interpolate(df.Expression('1 - cos(2*pi*sqrt(x[0]*x[0]+x[1]*x[1])/L)',L=self.system_size, pi=np.pi, degree=1), self.function_space.sub(2).collapse())
# add noise
noise_u = self.noise_level * (2*np.random.random(u0.vector().size())-1)
u0.vector()[:] = u0.vector()[:] + noise_u
# noise_rho = self.noise_level * (2*np.random.random(rho0.vector().size())-1)
# rho0.vector()[:] = rho0.vector()[:] + noise_rho
# ic for rho
r2 = "+".join(['x['+str(i)+']*x['+str(i)+']' for i in range(self.dimension)])
# rho0 = df.interpolate(df.Constant(0.0), self.function_space.sub(2).collapse())
rho0 = 'a*x[0]*x[0]*(1-tanh((sqrt(%s) - r0)/w))' %r2
rho0 = df.interpolate(df.Expression(rho0, a=self.average_rho, r0=0.5, w=0.2, degree=1), self.function_space.sub(2).collapse())
# add noise
noise_rho = self.noise_level * (2*np.random.random(rho0.vector().size())-1)
rho0.vector()[:] = rho0.vector()[:] + noise_rho
# ic for c
if self.morphogen:
c0 = df.interpolate(df.Expression('1 + 0.2*cos(2*pi*sqrt(x[0]*x[0]+x[1]*x[1])/L)',L=self.system_size, pi=np.pi, degree=1), self.function_space.sub(3).collapse())
c0 = 'a*(1 - tanh((sqrt(%s) - r0)/w))/2.0' % r2
# c0 = df.interpolate(df.Expression(c0, L=self.system_size, pi=np.pi, degree=1), self.function_space.sub(3).collapse())
c0 = df.interpolate(df.Expression(c0, a=self.average_rho, r0=0.5, w=0.1, degree=1), self.function_space.sub(3).collapse())
# add noise
# noise_c = self.noise_level * (2*np.random.random(c0.vector().size())-1)
# c0.vector()[:] = c0.vector()[:] + noise_c
noise_c = self.noise_level * (2*np.random.random(c0.vector().size())-1)
c0.vector()[:] = c0.vector()[:] + noise_c
else:
c0 = df.Constant(1.0)
......@@ -152,19 +162,6 @@ class Growing_Domain(object):
else:
self.form = (uform + vform + rhoform) * df.dx
def save_data_uvrho(self):
u, v, rho = self.f0.split(deepcopy=True)
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
def save_data_uvrhoc(self):
u, v, rho, c = self.f0.split(deepcopy=True)
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
self.cFile.write_checkpoint(c, 'concentration', self.time, append=True)
def solve(self,DIR=''):
# for saving data
self.uFile = df.XDMFFile(os.path.join(DIR, '%s_displacement.xdmf' % self.timestamp))
......@@ -180,27 +177,45 @@ class Growing_Domain(object):
self.time = 0.0
savesteps = int(self.savetime/self.timestep)
maxsteps = int(self.maxtime/self.timestep)
for steps in range(1, maxsteps + 1):
if self.morphogen:
u, v, rho, c = self.f0.split(deepcopy=True)
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
self.cFile.write_checkpoint(c, 'concentration', self.time, append=True)
else:
u, v, rho = self.f0.split(deepcopy=True)
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
for steps in progressbar.progressbar(range(1, maxsteps + 1)):
# solve
df.solve(self.form == 0, self.f, self.bc)
# update
df.assign(self.f0, self.f)
self.f0.assign(self.f)
if self.morphogen:
u, v, rho, c = self.f.split(deepcopy=True)
u, v, rho, c = self.f0.split(deepcopy=True)
if steps % savesteps == 0:
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
self.cFile.write_checkpoint(c, 'concentration', self.time, append=True)
else:
u, v, rho = self.f.split(deepcopy=True)
u, v, rho = self.f0.split(deepcopy=True)
if steps % savesteps == 0:
self.savedata()
self.uFile.write_checkpoint(u, 'displacement', self.time, append=True)
self.vFile.write_checkpoint(v, 'velocity', self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.time, append=True)
# move mesh
dr = df.project(u, self.function_space.sub(0).collapse())
df.ALE.move(self.mesh, dr)
# update time
self.time += self.timestep
# move mesh
# displacement = df.project(self.v*self.timestep, self.function_space)
df.ALE.move(self.mesh, u)
self.uFile.close()
self.vFile.close()
self.rhoFile.close()
self.rhoFile.close() # def save_data_uvrho(self):
if self.morphogen:
self.cFile.close()
......
growing_domain/full_model/viz_growing_domain.py
......@@ -4,14 +4,13 @@ import vedo as vd
import os
import h5py
from matplotlib.widgets import Slider
import progressbar
import matplotlib.pyplot as plt
from tempfile import TemporaryDirectory
def get_data(params, DIR=''):
savesteps = int(params['maxtime']/params['savetime'])
times = np.arange(savesteps+1) * params['savetime']
# Read mesh geometry from h5 file
var = 'density'
h5 = h5py.File(os.path.join(DIR, '%s_%s.h5' % (params['timestamp'], var)), "r")
......@@ -24,8 +23,7 @@ def get_data(params, DIR=''):
geometry = np.array(geometry)
if params['dimension']==1:
geometry, zeros= np.dsplit(geometry, 2)
print(geometry, topology)
raise SystemExit
# create a mesh
if params['dimension']==1:
mesh = df.IntervalMesh(params['resolution'], 0, params['system_size'])
......@@ -44,35 +42,77 @@ def get_data(params, DIR=''):
editor.close()
# Read concentration data
concentration = np.zeros((len(times), len(geometry[0])))
cFile = os.path.join(DIR, '%s_%s.xdmf' % (params['timestamp'],var))
with df.XDMFFile(cFile) as cFile:
for steps in range(savesteps+1):
if params['dimension']==1:
mesh.coordinates()[:] = geometry[steps]
VFS = df.FunctionSpace(mesh, 'P', 1)
c = df.Function(VFS)
cFile.read_checkpoint(c, var, steps)
concentration[steps] = c.compute_vertex_values(mesh)
SFS = df.FunctionSpace(mesh, 'P', 1)
VFS = df.VectorFunctionSpace(mesh, 'P', 1)
ui, vi, rhoi = df.Function(VFS), df.Function(VFS), df.Function(SFS)
u = np.zeros((len(times), mesh.num_vertices(), params['dimension']))
v = np.zeros_like(u)
rho = np.zeros((len(times), mesh.num_vertices()))
uFile = df.XDMFFile(os.path.join(DIR, '%s_displacement.xdmf' % params['timestamp']))
vFile = df.XDMFFile(os.path.join(DIR, '%s_velocity.xdmf' % params['timestamp']))
rhoFile = df.XDMFFile(os.path.join(DIR, '%s_density.xdmf' % params['timestamp']))
if params['morphogen']:
ci = df.Function(SFS)
c = np.zeros_like(rho)
cFile = df.XDMFFile(os.path.join(DIR, '%s_concentration.xdmf' % params['timestamp']))
for steps in progressbar.progressbar(range(savesteps+1)):
uFile.read_checkpoint(ui, 'displacement', steps)
vFile.read_checkpoint(vi, 'velocity', steps)
rhoFile.read_checkpoint(rhoi, 'density', steps)
u_vec = ui.compute_vertex_values(mesh)
u[steps] = u_vec.reshape(params['dimension'], int(u_vec.shape[0]/params['dimension'])).T
v_vec = vi.compute_vertex_values(mesh)
v[steps] = v_vec.reshape(params['dimension'], int(v_vec.shape[0]/params['dimension'])).T
rho[steps] = rhoi.compute_vertex_values(mesh)
if params['morphogen']:
cFile.read_checkpoint(ci, 'concentration', steps)
c[steps] = ci.compute_vertex_values(mesh)
uFile.close()
vFile.close()
rhoFile.close()
if params['morphogen']:
cFile.close()
return (times, topology, geometry, u, v, rho, c)
else:
return (times, topology, geometry, u, v, rho)
return (times, geometry, topology, concentration)
def visualize(params, DIR='', offscreen=False):
(times, geometry, topology, concentration) = get_data(params, DIR)
if params['morphogen']:
(times, topology, geometry, u, v, rho, c) = get_data(params, DIR)
else:
(times, topology, geometry, u, v, rho) = get_data(params, DIR)
radius = np.linalg.norm(geometry, axis=2)
if params['dimension']==1:
fig, axc = plt.subplots(1,1, figsize=(8,8))
if params['morphogen']:
fig, (axrho, axc) = plt.subplots(2,1, sharex=True, figsize=(8,8))
axc.set_xlabel(r'$x$')
axc.set_ylabel(r"$c(x,t)$")
axc.set_xlim(np.min(radius), np.max(radius))
axc.set_ylim(np.min(concentration), np.max(concentration))
axc.set_ylabel(r'$c(x,t)$')
cplot, = axc.plot(radius[0], concentration[0])
axc.set_ylim(np.min(c), np.max(c))
else:
fig, axrho = plt.subplots(1,1, sharex=True, figsize=(8,8))
axrho.set_xlabel(r'$x$')
axrho.set_ylabel(r"$\rho(x,t)$")
axrho.set_xlim(np.min(radius), np.max(radius))
axrho.set_ylim(np.min(rho), np.max(rho))
rhoplot, = axrho.plot(radius[0], rho[0],'o',ms=3)
if params['morphogen']:
cplot, = axc.plot(radius[0], c[0])
def update(value):
ti = np.abs(times-value).argmin()
cplot.set_ydata(concentration[ti])
rhoplot.set_ydata(rho[ti])
rhoplot.set_xdata(radius[ti])
if params['morphogen']:
cplot.set_ydata(c[ti])
cplot.set_xdata(radius[ti])
plt.draw()
......@@ -90,16 +130,16 @@ def visualize(params, DIR='', offscreen=False):
scalar_cmap = 'viridis'
geometry = np.dstack((geometry, np.zeros(geometry.shape[0:2])))
cmin, cmax = np.min(concentration), np.max(concentration)
rhomin, rhomax = np.min(rho), np.max(rho)
plotter = vd.plotter.Plotter(axes=0)
poly = vd.utils.buildPolyData(geometry[0], topology)
scalar_actor = vd.mesh.Mesh(poly)
#scalar_actor.computeNormals(points=True, cells=True)
scalar_actor.pointdata['concentration'] = concentration[0]
scalar_actor.cmap(scalar_cmap, concentration[0], vmin=cmin, vmax=cmax, n=n_cmap_vals)
scalar_actor.add_scalarbar(title = r'$c_{numerical}$',
scalar_actor.pointdata['density'] = rho[0]
scalar_actor.cmap(scalar_cmap, rho[0], vmin=rhomin, vmax=rhomax, n=n_cmap_vals)
scalar_actor.add_scalarbar(title = r'$\rho$',
pos=(0.8, 0.04), nlabels=2,
# titleYOffset=15, titleFontSize=28, size=(100, 600)
)
......@@ -107,7 +147,7 @@ def visualize(params, DIR='', offscreen=False):
def update(idx):
scalar_actor.points(pts=geometry[idx], transformed=False)
scalar_actor.pointdata['concentration'] = concentration[idx]
scalar_actor.pointdata['density'] = rho[idx]
def slider_update(widget, event):
value = widget.GetRepresentation().GetValue()
......@@ -119,6 +159,7 @@ def visualize(params, DIR='', offscreen=False):
value=times[0], title=r"$t/\tau$")
vd.show(interactive=(not offscreen), zoom=0.8)
if offscreen:
FPS = 10
movFile = '%s_numerical.mov' % params['timestamp']
......@@ -139,16 +180,16 @@ def visualize(params, DIR='', offscreen=False):
tmp_dir.cleanup()
# c(r,t) vs r
fig1, axc1 = plt.subplots(1,1, figsize=(8,8))
axc1.set_xlabel(r'$r$')
axc1.set_xlim(np.min(radius), np.max(radius))
axc1.set_ylim(np.min(concentration), np.max(concentration))
axc1.set_ylabel(r'$c(r,t)$')
cplot, = axc1.plot(radius[0], concentration[0],'o', ms=3)
fig1, axrho1 = plt.subplots(1,1, figsize=(8,8))
axrho1.set_xlabel(r'$r$')
axrho1.set_xlim(np.min(radius), np.max(radius))
axrho1.set_ylim(np.min(rho), np.max(rho))
axrho1.set_ylabel(r'$c(r,t)$')
cplot, = axrho1.plot(radius[0], rho[0],'o', ms=3)
def update(value):
ti = np.abs(times-value).argmin()
cplot.set_ydata(concentration[ti])
cplot.set_ydata(rho[ti])
cplot.set_xdata(radius[ti])
plt.draw()
......
growing_domain/given_v_get_rho_c/1D_growth/time_dependent_alpha_exp_growth.py.py deleted 100644 → 0
import dolfin as df
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import progressbar
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
def advection_diffusion(Nx, L, Nt, tmax, D, tstop, m):
# mesh, function space, function, test function
mesh = df.IntervalMesh(Nx, 0, L)
SFS = df.FunctionSpace(mesh, 'P', 1)
c = df.Function(SFS)
tc = df.TestFunction(SFS)
# x and t arrays
times = np.linspace(0, tmax, Nt+1)
dt = times[1] - times[0]
# initial condition
c0 = df.Function(SFS)
c0.interpolate(df.Expression('1 + 0.2 * cos(m * pi*x[0]/L)', m = m, pi=np.pi, L=L, degree=1))
# arrays
c_array = np.zeros((Nt+1, Nx+1))
x_array = np.zeros((Nt+1, Nx+1))
x_array[0] = mesh.coordinates()[:, 0]
c_array[0] = c0.compute_vertex_values(mesh)
# velocity
u = df.Expression('(t < tstop ? alpha0 : 0)*x[0]', alpha0 = alpha0, tstop=tstop, t=0, degree=0)
uh = df.project(u, SFS)
# form
cform = (df.inner((c - c0)/dt, tc)
+ D * df.inner(df.nabla_grad(c), df.nabla_grad(tc))
+ df.inner((uh*c).dx(0), tc) )* df.dx
# solve
for i in progressbar.progressbar(range(1, Nt+1)):
u.t = times[i]
uh.assign(df.project(u, SFS))
df.solve(cform == 0, c)
c_array[i] = c.compute_vertex_values(mesh)
c0.assign(c)
df.ALE.move(mesh, df.project(uh*dt, SFS))
x_array[i] = mesh.coordinates()[:,0]
return c_array, x_array
# plot c(x,t) numerical and analytical for given dt
dx, L, dt, tmax, D, m = 0.01, 1, 0.01, 100, 0.01, 2
alpha0, tstop = 0.01, 3
Nx = int(L/dx)
Nt = int(tmax/dt)
times = np.linspace(0, tmax, Nt+1)
# numerical solution
c, x = advection_diffusion(Nx, L, Nt, tmax, D, tstop, m)
# analytical solution
c_exact = np.zeros((Nt+1, Nx+1))
for j in range(0, len(times)):
if times[j] <= tstop:
# diffusion-advection on moving domain with velocity alpha0*x
alpha = alpha0
l = L * np.exp(alpha * times[j])
beta = (-D * m**2 * np.pi**2 /(2 *alpha * L**2)) * (1 - np.exp(-2 * alpha * times[j]))
c_exact[j] = np.exp(-alpha * times[j])* (1 + 0.2 * np.cos(m * np.pi*x[j]/l) * np.exp(beta))
else:
# diffusion on fixed domain of length L = L0*exp(alpha0 * tc) with initial condition to be the profile at tc
l = L * np.exp(alpha0 * tstop)
beta = -D * m**2 * np.pi**2*(times[j] - tstop)/l**2 - np.pi**2 * D * m**2/(2*L**2*alpha0) * (1 - np.exp(-2 *alpha0 *tstop))
c_exact[j] = np.exp(-alpha0 * tstop) * (1 + 0.2 * np.exp(beta) * np.cos(m * np.pi * x[j]/l))
fig, ax = plt.subplots(1,1,figsize=(8,6))
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$c(x,t)$')
ax.set_xlim(np.min(x), np.max(x))
ax.set_ylim(min(np.min(c), np.min(c_exact)), max(np.max(c), np.max(c_exact)))
ax.grid(True)
cplot, = ax.plot(x[0], c[0], '--',label = 'Numerical solution')
c_exactplot, = ax.plot(x[0], c_exact[0],label = 'Exact solution')
def update(value):
ti = np.abs(times-value).argmin()
cplot.set_xdata(x[ti])
cplot.set_ydata(c[ti])
c_exactplot.set_xdata(x[ti])
c_exactplot.set_ydata(c_exact[ti])
plt.draw()
sax = plt.axes([0.1, 0.92, 0.7, 0.02])
slider = Slider(sax, r'$t/\tau$', min(times), max(times),
valinit=min(times), valfmt='%3.1f',
fc='#999999')
slider.drawon = False
slider.on_changed(update)
ax.legend(loc=0)
plt.show()
growing_domain/given_v_get_rho_c/growing_domain_diffusion/diffusion_on_growing_domain.py
import dolfin as df
import numpy as np
# import progressbar
import progressbar
import scipy as sc
import os
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
......@@ -66,7 +65,7 @@ class GrowthDiffusion(object):
cFile.write_checkpoint(self.c0, 'concentration', self.time)
# time stepping
for steps in range(1, maxsteps + 1):
for steps in progressbar.progressbar(range(1, maxsteps + 1)):
# get velocity
self.sigma.t = self.time
self.velocity.assign(df.project(self.sigma*self.growth_direction, self.VFS))
......
growth_parameters.json deleted 100644 → 0
{
"resolution" : 32,
"system_size_by_2PI" : 1 ,
"elasticity" : 1.0,
"viscosity" : 1.0,
"friction" : 1.0,
"lamda": 19.0,
"diffusion_rho" : 1.0,
"turnover_rho" : 0.0,
"average_rho" : 1.0,
"saturation_rho" : 1.0,
"diffusion_c" : 1.0,
"turnover_c" : 1.0,
"average_c" : 1.0,
"timestep" : 0.01,
"maxtime" : 10.0
}
moving_domain/linear_growth.py deleted 100644 → 0
import dolfin as df
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import progressbar
df.set_log_level(df.LogLevel.ERROR)
df.parameters['form_compiler']['optimize'] = True
# parameters
tmax, dt, L, dx, b, m, D = 20, 0.01, 1, 0.01, 0.1, 2, 0.1
Nt = int(tmax/dt)
Nx = int(L/dx)
# mesh, function space, functions
mesh = df.IntervalMesh(Nx, 0, L)
function_space = df.FunctionSpace(mesh, 'P', 1)
c, tc = df.Function(function_space), df.TestFunction(function_space)
# initial condition
c0 = df.interpolate(df.Expression('1 + 0.2*cos(m * pi * x[0]/L)', pi = np.pi, L = L, m = m, degree=1), function_space)
# arrays
times = np.linspace(0, tmax, Nt + 1)
x_array = np.zeros((Nt+1, Nx+1))
x_array[0] = mesh.coordinates()[:, 0]
c_array = np.zeros((Nt+1, Nx+1))
c_array[0] = c0.compute_vertex_values(mesh)
# velocity
v = df.Expression('b*x[0]/(L + b *t)', b=b, L=L, t=0, degree=0)
vh = df.project(v, function_space)
# form
cform = (df.inner((c - c0)/dt, tc)
+ D * df.inner((c).dx(0), (tc).dx(0))
+ df.inner((vh*c0).dx(0), tc)
)* df.dx
# time stepping
for i in progressbar.progressbar(range(1, Nt+1)):
v.t = times[i]
vh.assign(df.project(v, function_space))
df.solve(cform == 0, c)
c_array[i] = c.compute_vertex_values(mesh)
c0.assign(c)
df.ALE.move(mesh, df.project(vh*dt, function_space))
x_array[i] = mesh.coordinates()[:, 0]
# exact solution
c_exact = np.zeros((Nt + 1, Nx + 1))
for j in range(0, Nt+1):
l = L + b * times[j]
c_exact[j] = (L/l) * (1 + 0.2 * np.cos(m * np.pi * x_array[j]/l) * np.exp(-m**2 * np.pi**2 * D * times[j]/(L * l)))
# plotting
fig, ax = plt.subplots(1,1,figsize=(8,6))
ax.set_xlabel(r'$x$')
ax.set_ylabel(r'$c(x,t)$')
ax.set_xlim(np.min(x_array), np.max(x_array))
ax.set_ylim(min(np.min(c_exact), np.min(c_array)), max(np.max(c_array), np.max(c_exact)))
ax.grid(True)
cplot, = ax.plot(x_array[0], c_array[0], '--',label = 'Numerical solution')
c_exactplot, = ax.plot(x_array[0], c_exact[0],label = 'Exact solution')
def update(value):
ti = np.abs(times-value).argmin()
cplot.set_xdata(x_array[ti])
cplot.set_ydata(c_array[ti])
c_exactplot.set_xdata(x_array[ti])
c_exactplot.set_ydata(c_exact[ti])
plt.draw()
sax = plt.axes([0.1, 0.92, 0.7, 0.02])
slider = Slider(sax, r'$t/\tau$', min(times), max(times),
valinit=min(times), valfmt='%3.1f',
fc='#999999')
slider.drawon = False
slider.on_changed(update)
ax.legend(loc=0)
plt.show()
\ No newline at end of file
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