def viscoElasticUpdater_bgvel(t, y, wdict):
#interior function for incompressible background flow only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
N = pdict['N']
M = pdict['M']
l2 = np.reshape(y[range(2 * N * M)], (N * M, 2))
l3 = np.reshape(l2, (N, M, 2))
P2 = np.reshape(y[(2 * N * M):], (N * M, 2, 2))
P3 = np.reshape(P2, (N, M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P3, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
#calculate new velocities at all points of interest
ub, gradub = wdict['myVelocity'](pdict, l2)
lt0 = pdict['gridspc']**2 * CM.matmult(pdict['eps_grid'], pdict['mu'], l2,
l2, Pd)
# reshape the velocities on the grid
lt3 = np.reshape(lt0, (N, M, 2))
lt = ub + lt0
# calculate new stress time derivatives
gradlt = SD2D.vectorGrad(lt3, pdict['gridspc'], N, M)
gradlt = np.reshape(gradlt, (N * M, 2, 2))
Pt = CM.stressDeriv(pdict['Wi'], gradub, gradlt, F, P2)
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) #grad(Stokeslet) method
# Finv = CM.matinv2x2(F) #first grad(u) method
# Pt = np.zeros((N*M,2,2)) #first grad(u) method
# for j in range(N*M):
# Pt[j,:,:] = np.dot(gradub[j,:,:],P2[j,:,:]) + np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
return np.append(lt, Pt.flatten())
def veExtensionUpdater(t, y, pdict):
#interior function for incompressible background flow only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
N = pdict['N']
M = pdict['M']
l = y[range(2 * N * M)]
l2col = np.reshape(l, (N * M, 2))
l3D = np.reshape(l, (N, M, 2))
P = np.reshape(y[(2 * N * M):], (N, M, 2, 2))
Ps = np.reshape(P, (N * M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3D, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
Finv = CM.matinv2x2(F)
#calculate new velocities at all points of interest (Lagrangian points and force points)
ub, gradub = pdict['myVelocity'](pdict, l, l2col)
lt = ub + pdict['gridspc']**2 * CM.matmult(pdict['eps'], pdict['mu'],
l2col, l2col, Pd)
#calculate new stress time derivatives
gradlt = pdict['gridspc']**2 * CM.derivop(pdict['eps'], pdict['mu'], l2col,
l2col, Pd, F)
Pt = np.zeros((N * M, 2, 2))
for j in range(N * M):
Pt[j, :, :] = np.dot(gradub[j, :, :], Ps[j, :, :]) + np.dot(
np.dot(gradlt[j, :, :], Finv[j, :, :]), Ps[j, :, :]) - (
1. / pdict['Wi']) * (Ps[j, :, :] - Finv[j, :, :].transpose())
return np.append(lt, Pt.flatten())
def simresults(basename, basedir):
'''Retrieve approximate solution from saved output'''
mydict = fileops.loadPickle(basename=basename, basedir=basedir)
l = mydict['l']
S = mydict['S']
F = []
Finv = []
P = []
N = l[0].shape[0]
M = l[0].shape[1]
for k in range(len(mydict['t'])):
Ft = SD2D.vectorGrad(l[k], mydict['pdict']['gridspc'], N, M)
Ftemp = np.reshape(Ft, (N * M, 2, 2))
Ftinv = CM.matinv2x2(Ftemp)
Ftinv = np.reshape(Ftinv, (N, M, 2, 2))
F.append(Ft.copy())
Finv.append(Ftinv.copy())
stress = np.zeros((N, M, 2, 2))
for j in range(N):
for m in range(M):
stress[j,
m, :, :] = S[k][j,
m, :, :] * Ftinv[j,
m, :, :].transpose()
P.append(stress.copy())
return l, P, S, F, Finv, mydict
def viscoElasticUpdaterKernelDeriv(t, y, pdict):
#interior function for force pts only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
if 'forcedict' not in pdict.keys():
pdict['forcedict'] = {}
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y) / 2 - N * M - 2 * N * M
fpts = np.reshape(y[:2 * Q], (Q, 2))
l = y[range(2 * Q, 2 * Q + 2 * N * M)]
l2col = np.reshape(l, (N * M, 2))
l3D = np.reshape(l, (N, M, 2))
allpts = y[:2 * Q + 2 * N * M] #both force points and Lagrangian points
ap = np.reshape(allpts, (Q + N * M, 2))
P = np.reshape(y[(2 * Q + 2 * N * M):], (N, M, 2, 2))
Ps = np.reshape(P, (N * M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate spring forces
f = pdict['myForces'](fpts, pdict['xr'], pdict['K'], **pdict['forcedict'])
#calculate deformation matrix and its inverse
gl = SD2D.vectorGrad(l3D, pdict['gridspc'], N, M)
gls = np.reshape(gl, (N * M, 2, 2))
igls = CM.matinv2x2(gls)
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = pdict['gridspc']**2 * CM.matmult(
pdict['eps'], pdict['mu'], ap, l2col, Pd) + CM.matmult(
pdict['eps'], pdict['mu'], ap, fpts, f)
#calculate new stress time derivatives
glst = pdict['gridspc']**2 * CM.derivop(
pdict['eps'], pdict['mu'], l2col, l2col, Pd, gls) + CM.derivop(
pdict['eps'], pdict['mu'], l2col, fpts, f, gls)
Pt = np.zeros((N * M, 2, 2))
for j in range(N * M):
Pt[j, :, :] = np.dot(np.dot(glst[j, :, :], igls[j, :, :]),
Ps[j, :, :]) - (1. / pdict['Wi']) * (
Ps[j, :, :] - igls[j, :, :].transpose())
return np.append(lt, Pt.flatten())
def viscoElasticUpdater_force(t, y, wdict):
#interior function for force pts only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
pdict = wdict['pdict']
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y) / 2 - N * M - 2 * N * M
fpts = np.reshape(y[:2 * Q], (Q, 2))
l2 = np.reshape(y[range(2 * Q, 2 * Q + 2 * N * M)], (N * M, 2))
l3 = np.reshape(l2, (N, M, 2))
allpts = np.reshape(
y[:2 * Q + 2 * N * M],
(Q + N * M, 2)) # both force points and Lagrangian points
P2 = np.reshape(y[(2 * Q + 2 * N * M):], (N * M, 2, 2))
P3 = np.reshape(P2, (N, M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P3, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate spring forces
f = wdict['myForces'](fpts, **pdict['forcedict'])
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = pdict['gridspc']**2 * CM.matmult(
pdict['eps_grid'], pdict['mu'], allpts, l2, Pd) + CM.matmult(
pdict['eps_obj'], pdict['mu'], allpts, fpts, f)
# reshape the velocities on the grid
lt3 = np.reshape(lt[2 * Q:], (N, M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
#calculate new stress time derivatives
# gradlt = pdict['gridspc']**2*CM.derivop(pdict['eps_grid'],pdict['mu'],l2,l2,Pd,F) + CM.derivop(pdict['eps_obj'],pdict['mu'],l2,fpts,f,F) #grad(Stokeslet) method
gradlt = SD2D.vectorGrad(lt3, pdict['gridspc'], N, M)
gradlt = np.reshape(gradlt, (N * M, 2, 2))
# Finv = CM.matinv2x2(F) # first grad(u) method
# Pt = np.zeros((N*M,2,2))
# for j in range(N*M):
# Pt[j,:,:] = np.dot(np.dot(gradlt[j,:,:],Finv[j,:,:]),P2[j,:,:]) - (1./pdict['Wi'])*(P2[j,:,:] - Finv[j,:,:].transpose())
Pt = CM.stressDeriv(pdict['Wi'], gradlt, F, P2)
return np.append(lt, Pt.flatten())
def stokesFlowUpdaterWithMarkers(t, y, wdict):
pdict = wdict['pdict']
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y) / 2 - N * M
fpts = np.reshape(y[:2 * Q], (Q, 2))
ap = np.reshape(y, (Q + N * M, 2))
#calculate spring forces
f = pdict['myForces'](fpts, **pdict['forcedict'])
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = CM.matmult(pdict['eps_obj'], pdict['mu'], ap, fpts, f)
return lt
def stokesFlowUpdater(t, y, wdict):
'''
t = current time, y = [fpts.flatten(), l.flatten(), P.flatten()], pdict
contains: K is spring constant, xr is resting position, blob is regularized
Stokeslet object, myForces is a function handle, forcedict is a dictionary
containing optional parameters for calculating forces.
'''
pdict = wdict['pdict']
pdict['forcedict']['t'] = t
Q = len(y) / 2
fpts = np.reshape(y, (Q, 2))
f = wdict['myForces'](fpts, **pdict['forcedict'])
yt = CM.matmult(pdict['eps_obj'], pdict['mu'], fpts, fpts, f)
return yt
def simresults(basename, basedir):
'''Retrieve approximate solution from saved output'''
mydict = loadPickle(basename, basedir)
l = mydict['l']
regridinds = findRegridTimes(l)
S=mydict['S']
P=[]
for k in range(len(mydict['t'])):
# N and M can change because of regridding
N = l[k].shape[0]
M = l[k].shape[1]
Ft = SD2D.vectorGrad(l[k],mydict['pdict']['gridspc'],N,M)
Ftemp = np.reshape(Ft,(N*M,2,2))
Ftinv = CM.matinv2x2(Ftemp)
Ftinv = np.reshape(Ftinv,(N,M,2,2))
stressP = np.zeros((N,M,2,2))
for j in range(N):
for m in range(M):
stressP[j,m,:,:] = S[k][j,m,:,:]*Ftinv[j,m,:,:].transpose()
P.append(stressP.copy())
return l, P, S, mydict, regridinds
def simresults(basename, basedir):
'''Retrieve approximate solution from saved output'''
mydict = fileops.loadPickle(basename=basename, basedir=basedir)
l = mydict['l']
S=mydict['S']
F=[]
Finv=[]
P=[]
N = l[0].shape[0]
M = l[0].shape[1]
for k in range(len(mydict['t'])):
Ft = SD2D.vectorGrad(l[k],mydict['pdict']['gridspc'],N,M)
Ftemp = np.reshape(Ft,(N*M,2,2))
Ftinv = CM.matinv2x2(Ftemp)
Ftinv = np.reshape(Ftinv,(N,M,2,2))
F.append(Ft.copy())
Finv.append(Ftinv.copy())
stress = np.zeros((N,M,2,2))
for j in range(N):
for m in range(M):
stress[j,m,:,:] = S[k][j,m,:,:]*Ftinv[j,m,:,:].transpose()
P.append(stress.copy())
return l, P, S, F, Finv, mydict