def solve_nse(A=None, M=None, J=None, JT=None,
fv=None, fp=None,
fvc=None, fpc=None, # TODO: this is to catch deprecated calls
fv_tmdp=None, fv_tmdp_params={},
fv_tmdp_memory=None,
iniv=None, lin_vel_point=None,
stokes_flow=False,
trange=None,
t0=None, tE=None, Nts=None,
V=None, Q=None, invinds=None, diribcs=None,
output_includes_bcs=False,
N=None, nu=None,
ppin=-1,
closed_loop=False, static_feedback=False,
feedbackthroughdict=None,
return_vp=False,
tb_mat=None, c_mat=None,
vel_nwtn_stps=20, vel_nwtn_tol=5e-15,
vel_pcrd_stps=4,
krylov=None, krpslvprms={}, krplsprms={},
clearprvdata=False,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
vfileprfx='', pfileprfx='',
return_dictofvelstrs=False,
return_dictofpstrs=False,
dictkeysstr=False,
comp_nonl_semexp=False,
return_as_list=False,
start_ssstokes=False,
**kw):
"""
solution of the time-dependent nonlinear Navier-Stokes equation
.. math::
M\\dot v + Av + N(v)v + J^Tp = f \n
Jv =g
using a Newton scheme in function space, i.e. given :math:`v_k`,
we solve for the update like
.. math::
M\\dot v + Av + N(v_k)v + N(v)v_k + J^Tp = N(v_k)v_k + f,
and trapezoidal rule in time. To solve an *Oseen* system (linearization
about a steady state) or a *Stokes* system, set the number of Newton
steps to one and provide a linearization point and an initial value.
Parameters
----------
lin_vel_point : dictionary, optional
contains the linearization point for the first Newton iteration
* Steady State: {{`None`: 'path_to_nparray'}, {'None': nparray}}
* Newton: {`t`: 'path_to_nparray'}
defaults to `None`
dictkeysstr : boolean, optional
whether the `keys` of the result dictionaries are strings instead \
of floats, defaults to `False`
fv_tmdp : callable f(t, v, dict), optional
time-dependent part of the right-hand side, set to zero if None
fv_tmdp_params : dictionary, optional
dictionary of parameters to be passed to `fv_tmdp`, defaults to `{}`
fv_tmdp_memory : dictionary, optional
memory of the function
output_includes_bcs : boolean, optional
whether append the boundary nodes to the computed and stored \
velocities, defaults to `False`
krylov : {None, 'gmres'}, optional
whether or not to use an iterative solver, defaults to `None`
krpslvprms : dictionary, optional
to specify parameters of the linear solver for use in Krypy, e.g.,
* initial guess
* tolerance
* number of iterations
defaults to `None`
krplsprms : dictionary, optional
parameters to define the linear system like
* preconditioner
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
stokes_flow : boolean, optional
whether to consider the Stokes linearization, defaults to `False`
start_ssstokes : boolean, optional
for your convenience, compute and use the steady state stokes solution
as initial value, defaults to `False`
Returns
-------
dictofvelstrs : dictionary, on demand
dictionary with time `t` as keys and path to velocity files as values
dictofpstrs : dictionary, on demand
dictionary with time `t` as keys and path to pressure files as values
vellist : list, on demand
list of the velocity solutions
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if fvc is not None or fpc is not None: # TODO: this is for catching calls
raise UserWarning('deprecated use of `rhsd_vfrc`, use only `fv`, `fp`')
if get_datastring is None:
get_datastring = get_datastr_snu
if paraviewoutput:
prvoutdict = dict(V=V, Q=Q, invinds=invinds, diribcs=diribcs,
vp=None, t=None, writeoutput=True, ppin=ppin)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' here
if trange is None:
trange = np.linspace(t0, tE, Nts+1)
if comp_nonl_semexp and lin_vel_point is not None:
raise UserWarning('I am not sure what you want! ' +
'set either `lin_vel_point=None` ' +
'or `comp_nonl_semexp=False`! \n' +
'as it is I will compute a linear case')
if return_dictofpstrs:
gpfvd = dict(V=V, M=M, A=A, J=J,
fv=fv, fp=fp,
diribcs=diribcs, invinds=invinds)
NV, NP = A.shape[0], J.shape[0]
if fv_tmdp is None:
def fv_tmdp(time=None, curvel=None, **kw):
return np.zeros((NV, 1)), None
if iniv is None:
if start_ssstokes:
# Stokes solution as starting value
(fv_tmdp_cont,
fv_tmdp_memory) = fv_tmdp(time=0, **fv_tmdp_params)
vp_stokes =\
lau.solve_sadpnt_smw(amat=A, jmat=J, jmatT=JT,
rhsv=fv + fv_tmdp_cont,
krylov=krylov, krpslvprms=krpslvprms,
krplsprms=krplsprms, rhsp=fp)
iniv = vp_stokes[:NV]
else:
raise ValueError('No initial value given')
datastrdict = dict(time=None, meshp=N, nu=nu,
Nts=trange.size-1, data_prfx=data_prfx)
if return_as_list:
clearprvdata = True # we want the results at hand
if clearprvdata:
datastrdict['time'] = '*'
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '__vel*'):
os.remove(fname)
for fname in glob.glob(cdatstr + '__p*'):
os.remove(fname)
def _atdct(cdict, t, thing):
if dictkeysstr:
cdict.update({'{0}'.format(t): thing})
else:
cdict.update({t: thing})
def _gfdct(cdict, t):
if dictkeysstr:
return cdict['{0}'.format(t)]
else:
return cdict[t]
if stokes_flow:
vel_nwtn_stps = 1
vel_pcrd_stps = 0
print 'Stokes Flow!'
elif lin_vel_point is None:
comp_nonl_semexp_inig = True
if not comp_nonl_semexp:
print('No linearization point given - explicit' +
' treatment of the nonlinearity in the first Iteration')
else:
cur_linvel_point = lin_vel_point
comp_nonl_semexp_inig = False
newtk, norm_nwtnupd, norm_nwtnupd_list = 0, 1, []
# check for previously computed velocities
if lin_vel_point is None and not stokes_flow:
try:
datastrdict.update(dict(time=trange[-1]))
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = dou.load_npa(cdatstr + '__norm_nwtnupd')
v_old = dou.load_npa(cdatstr + '__vel')
norm_nwtnupd_list.append(norm_nwtnupd)
print 'found vel files'
print 'norm of last Nwtn update: {0}'.format(norm_nwtnupd)
if norm_nwtnupd < vel_nwtn_tol and not return_dictofvelstrs:
return
elif norm_nwtnupd < vel_nwtn_tol:
datastrdict.update(dict(time=trange[0]))
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
try:
p_old = dou.load_npa(cdatstr + '__p')
dictofpstrs = {}
_atdct(dictofpstrs, trange[0], cdatstr+'__p')
except:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
_atdct(dictofpstrs, trange[0], cdatstr+'__p')
for t in trange[1:]:
# test if the vels are there
v_old = dou.load_npa(cdatstr + '__vel')
# update the dict
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
_atdct(dictofvelstrs, t, cdatstr + '__vel')
try:
p_old = dou.load_npa(cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
except:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
comp_nonl_semexp = False
except IOError:
norm_nwtnupd = 2
print 'no old velocity data found'
def _append_bcs_ornot(vvec):
if output_includes_bcs: # make the switch here for better readibility
vwbcs = dts.append_bcs_vec(vvec, vdim=V.dim(),
invinds=invinds, diribcs=diribcs)
return vwbcs
else:
return vvec
def _get_mats_rhs_ts(mmat=None, dt=None, var_c=None,
coeffmat_c=None,
coeffmat_n=None,
fv_c=None, fv_n=None,
umat_c=None, vmat_c=None,
umat_n=None, vmat_n=None,
impeul=False):
""" to be tweaked for different int schemes
"""
solvmat = M + 0.5*dt*coeffmat_n
rhs = M*var_c + 0.5*dt*(fv_n + fv_c - coeffmat_c*var_c)
if umat_n is not None:
matvec = lau.mm_dnssps
umat = 0.5*dt*umat_n
vmat = vmat_n
# TODO: do we really need a PLUS here??'
rhs = rhs + 0.5*dt*matvec(umat_c, matvec(vmat_c, var_c))
else:
umat, vmat = umat_n, vmat_n
return solvmat, rhs, umat, vmat
v_old = iniv # start vector for time integration in every Newtonit
datastrdict['time'] = trange[0]
cdatstr = get_datastring(**datastrdict)
dou.save_npa(_append_bcs_ornot(v_old), fstring=cdatstr + '__vel')
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
dictofpstrs = {}
_atdct(dictofpstrs, trange[0], cdatstr+'__p')
if return_as_list:
vellist = []
vellist.append(_append_bcs_ornot(v_old))
while (newtk < vel_nwtn_stps and norm_nwtnupd > vel_nwtn_tol):
if stokes_flow:
newtk = vel_nwtn_stps
elif comp_nonl_semexp_inig and not comp_nonl_semexp:
pcrd_anyone = False
print 'explicit treatment of nonl. for initial guess'
elif vel_pcrd_stps > 0 and not comp_nonl_semexp:
vel_pcrd_stps -= 1
pcrd_anyone = True
print 'Picard iterations for initial value -- {0} left'.\
format(vel_pcrd_stps)
elif comp_nonl_semexp:
pcrd_anyone = False
newtk = vel_nwtn_stps
print 'No Newton iterations - explicit treatment of the nonlin.'
else:
pcrd_anyone = False
newtk += 1
print 'Computing Newton Iteration {0}'.format(newtk)
v_old = iniv # start vector for time integration in every Newtonit
try:
if krpslvprms['krylovini'] == 'old':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
elif krpslvprms['krylovini'] == 'upd':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
vp_new = vp_old
cts_old = trange[1] - trange[0]
except (TypeError, KeyError):
pass # no inival for krylov solver required
vfile = dolfin.File(vfileprfx+'__timestep.pvd')
pfile = dolfin.File(pfileprfx+'__timestep.pvd')
prvoutdict.update(dict(vp=None, vc=iniv, t=trange[0],
pfile=pfile, vfile=vfile))
dou.output_paraview(**prvoutdict)
# ## current values_c for application of trap rule
if stokes_flow:
convc_mat_c = sps.csr_matrix((NV, NV))
rhs_con_c, rhsv_conbc_c = np.zeros((NV, 1)), np.zeros((NV, 1))
else:
if comp_nonl_semexp or comp_nonl_semexp_inig:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point, trange[0]))
except KeyError:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point, None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_c, rhs_con_c, rhsv_conbc_c = \
get_v_conv_conts(prev_v=iniv, invinds=invinds,
V=V, diribcs=diribcs, Picard=pcrd_anyone)
(fv_tmdp_cont,
fv_tmdp_memory) = fv_tmdp(time=0,
curvel=v_old,
memory=fv_tmdp_memory,
**fv_tmdp_params)
fvn_c = fv + rhsv_conbc_c + rhs_con_c + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_c = dou.load_npa(feedbackthroughdict[None]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[None]['w'])
# print '\nnorm of feedback: ', np.linalg.norm(mtxtb_c)
else:
mtxtb_c = dou.load_npa(feedbackthroughdict[0]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[0]['w'])
fvn_c = fvn_c + tb_mat * (tb_mat.T * w_c)
vmat_c = mtxtb_c.T
try:
umat_c = np.array(tb_mat.todense())
except AttributeError:
umat_c = tb_mat
else:
vmat_c = None
umat_c = None
norm_nwtnupd = 0
print 'time to go',
for tk, t in enumerate(trange[1:]):
cts = t - trange[tk]
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
sys.stdout.write("\rEnd: {1} -- now: {0:f}".format(t, trange[-1]))
sys.stdout.flush()
# prv_datastrdict = copy.deepcopy(datastrdict)
# coeffs and rhs at next time instance
if stokes_flow:
convc_mat_n = sps.csr_matrix((NV, NV))
rhs_con_n, rhsv_conbc_n = np.zeros((NV, 1)), np.zeros((NV, 1))
else:
if comp_nonl_semexp or comp_nonl_semexp_inig:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point, t))
except KeyError:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point,
None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_n, rhs_con_n, rhsv_conbc_n = \
get_v_conv_conts(prev_v=prev_v, invinds=invinds,
V=V, diribcs=diribcs, Picard=pcrd_anyone)
(fv_tmdp_cont,
fv_tmdp_memory) = fv_tmdp(time=t,
curvel=v_old,
memory=fv_tmdp_memory,
**fv_tmdp_params)
fvn_n = fv + rhsv_conbc_n + rhs_con_n + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_n = dou.load_npa(feedbackthroughdict[None]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[None]['w'])
# fb = np.dot(tb_mat*mtxtb_n.T, v_old)
# print '\nnorm of feedback: ', np.linalg.norm(fb)
# print '\nnorm of v_old: ', np.linalg.norm(v_old)
# print '\nnorm of feedthrough: ', np.linalg.norm(next_w)
else:
mtxtb_n = dou.load_npa(feedbackthroughdict[t]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[t]['w'])
fvn_n = fvn_n + tb_mat * (tb_mat.T * w_n)
vmat_n = mtxtb_n.T
try:
umat_n = np.array(tb_mat.todense())
except AttributeError:
umat_n = tb_mat
else:
vmat_n = None
umat_n = None
(solvmat, rhsv, umat,
vmat) = _get_mats_rhs_ts(mmat=M, dt=cts, var_c=v_old,
coeffmat_c=A + convc_mat_c,
coeffmat_n=A + convc_mat_n,
fv_c=fvn_c, fv_n=fvn_n,
umat_c=umat_c, vmat_c=vmat_c,
umat_n=umat_n, vmat_n=vmat_n)
try:
if krpslvprms['krylovini'] == 'old':
krpslvprms['x0'] = vp_old
elif krpslvprms['krylovini'] == 'upd':
vp_oldold = vp_old
vp_old = vp_new
krpslvprms['x0'] = vp_old + \
cts*(vp_old - vp_oldold)/cts_old
cts_old = cts
except (TypeError, KeyError):
pass # no inival for krylov solver required
vp_new = lau.solve_sadpnt_smw(amat=solvmat,
jmat=J, jmatT=JT,
rhsv=rhsv,
rhsp=fp,
krylov=krylov, krpslvprms=krpslvprms,
krplsprms=krplsprms,
umat=umat, vmat=vmat)
v_old = vp_new[:NV, ]
(umat_c, vmat_c, fvn_c,
convc_mat_c) = umat_n, vmat_n, fvn_n, convc_mat_n
dou.save_npa(_append_bcs_ornot(v_old), fstring=cdatstr + '__vel')
_atdct(dictofvelstrs, t, cdatstr + '__vel')
if return_dictofpstrs:
p_new = -1/cts*vp_new[NV:, ]
# p was flipped and scaled for symmetry
dou.save_npa(p_new, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_as_list:
vellist.append(_append_bcs_ornot(v_old))
prvoutdict.update(dict(vp=vp_new, t=t))
dou.output_paraview(**prvoutdict)
# integrate the Newton error
if stokes_flow or comp_nonl_semexp or comp_nonl_semexp_inig:
norm_nwtnupd = [None]
else:
if len(prev_v) > len(invinds):
prev_v = prev_v[invinds, :]
norm_nwtnupd += cts * m_innerproduct(M, v_old - prev_v)
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
norm_nwtnupd_list.append(norm_nwtnupd[0])
print '\nnorm of current Newton update: {}'.format(norm_nwtnupd)
comp_nonl_semexp = False
comp_nonl_semexp_inig = False
cur_linvel_point = dictofvelstrs
if return_dictofvelstrs:
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
elif return_as_list:
return vellist
else:
return
def solve_steadystate_nse(A=None, J=None, JT=None, M=None,
fv=None, fp=None,
V=None, Q=None, invinds=None, diribcs=None,
return_vp=False, ppin=-1,
N=None, nu=None,
vel_pcrd_stps=10, vel_pcrd_tol=1e-4,
vel_nwtn_stps=20, vel_nwtn_tol=5e-15,
clearprvdata=False,
vel_start_nwtn=None,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
save_intermediate_steps=False,
vfileprfx='', pfileprfx='',
**kw):
"""
Solution of the steady state nonlinear NSE Problem
using Newton's scheme. If no starting value is provided, the iteration
is started with the steady state Stokes solution.
Parameters
----------
A : (N,N) sparse matrix
stiffness matrix aka discrete Laplacian, note the sign!
M : (N,N) sparse matrix
mass matrix
J : (M,N) sparse matrix
discrete divergence operator
JT : (N,M) sparse matrix, optional
discrete gradient operator, set to J.T if not provided
fv, fp : (N,1), (M,1) ndarrays
right hand sides restricted via removing the boundary nodes in the
momentum and the pressure freedom in the continuity equation
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
return_vp : boolean, optional
whether to return also the pressure, defaults to `False`
vel_pcrd_stps : int, optional
Number of Picard iterations when computing a starting value for the
Newton scheme, cf. Elman, Silvester, Wathen: *FEM and fast iterative
solvers*, 2005, defaults to `100`
vel_pcrd_tol : real, optional
tolerance for the size of the Picard update, defaults to `1e-4`
vel_nwtn_stps : int, optional
Number of Newton iterations, defaults to `20`
vel_nwtn_tol : real, optional
tolerance for the size of the Newton update, defaults to `5e-15`
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if get_datastring is None:
get_datastring = get_datastr_snu
if JT is None:
JT = J.T
NV = J.shape[1]
#
# Compute or load the uncontrolled steady state Navier-Stokes solution
#
norm_nwtnupd_list = []
vel_newtk, norm_nwtnupd = 0, 1
# a dict to be passed to the get_datastring function
datastrdict = dict(time=None, meshp=N, nu=nu,
Nts=None, data_prfx=data_prfx)
if clearprvdata:
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '*__vel*'):
os.remove(fname)
try:
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = dou.load_npa(cdatstr + '__norm_nwtnupd')
vel_k = dou.load_npa(cdatstr + '__vel')
norm_nwtnupd_list.append(norm_nwtnupd)
print 'found vel files'
print 'norm of last Nwtn update: {0}'.format(norm_nwtnupd)
if norm_nwtnupd < vel_nwtn_tol:
if not return_vp:
return vel_k, norm_nwtnupd_list
else:
pfv = get_pfromv(v=vel_k[:NV, :], V=V, M=M, A=A, J=J, fv=fv,
invinds=invinds, diribcs=diribcs)
return (np.vstack([vel_k, pfv]), norm_nwtnupd_list)
except IOError:
print 'no old velocity data found'
norm_nwtnupd = None
if paraviewoutput:
cdatstr = get_datastring(**datastrdict)
vfile = dolfin.File(vfileprfx+'__steadystates.pvd')
pfile = dolfin.File(pfileprfx+'__steadystates.pvd')
prvoutdict = dict(V=V, Q=Q, vfile=vfile, pfile=pfile,
invinds=invinds, diribcs=diribcs, ppin=ppin,
vp=None, t=None, writeoutput=True)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' here
NV = A.shape[0]
if vel_start_nwtn is None:
vp_stokes = lau.solve_sadpnt_smw(amat=A, jmat=J, jmatT=JT,
rhsv=fv, rhsp=fp)
vp_stokes[NV:] = -vp_stokes[NV:]
# pressure was flipped for symmetry
# save the data
cdatstr = get_datastring(**datastrdict)
dou.save_npa(vp_stokes[:NV, ], fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_stokes))
dou.output_paraview(**prvoutdict)
# Stokes solution as starting value
vp_k = vp_stokes
vel_k = vp_stokes[:NV, ]
else:
vel_k = vel_start_nwtn
# Picard iterations for a good starting value for Newton
for k in range(vel_pcrd_stps):
(convc_mat,
rhs_con, rhsv_conbc) = get_v_conv_conts(prev_v=vel_k, invinds=invinds,
V=V, diribcs=diribcs,
Picard=True)
vp_k = lau.solve_sadpnt_smw(amat=A+convc_mat, jmat=J, jmatT=JT,
rhsv=fv+rhs_con+rhsv_conbc,
rhsp=fp)
normpicupd = np.sqrt(m_innerproduct(M, vel_k-vp_k[:NV, :]))[0]
print 'Picard iteration: {0} -- norm of update: {1}'\
.format(k+1, normpicupd)
vel_k = vp_k[:NV, ]
vp_k[NV:] = -vp_k[NV:]
# pressure was flipped for symmetry
if normpicupd < vel_pcrd_tol:
break
# Newton iteration
while (vel_newtk < vel_nwtn_stps
and (norm_nwtnupd is None or
norm_nwtnupd > vel_nwtn_tol or
norm_nwtnupd == np.array(None))):
vel_newtk += 1
cdatstr = get_datastring(**datastrdict)
(convc_mat,
rhs_con, rhsv_conbc) = get_v_conv_conts(vel_k, invinds=invinds,
V=V, diribcs=diribcs)
vp_k = lau.solve_sadpnt_smw(amat=A+convc_mat, jmat=J, jmatT=JT,
rhsv=fv+rhs_con+rhsv_conbc,
rhsp=fp)
norm_nwtnupd = np.sqrt(m_innerproduct(M, vel_k - vp_k[:NV, :]))[0]
vel_k = vp_k[:NV, ]
vp_k[NV:] = -vp_k[NV:]
# pressure was flipped for symmetry
print 'Steady State NSE: Newton iteration: {0} -- norm of update: {1}'\
.format(vel_newtk, norm_nwtnupd)
dou.save_npa(vel_k, fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_k))
dou.output_paraview(**prvoutdict)
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
dou.output_paraview(**prvoutdict)
# savetomatlab = True
# if savetomatlab:
# export_mats_to_matlab(E=None, A=None, matfname='matexport')
if return_vp:
return vp_k, norm_nwtnupd_list
else:
return vel_k, norm_nwtnupd_list
def solve_steadystate_nse(A=None,
J=None,
JT=None,
M=None,
fv=None,
fp=None,
V=None,
Q=None,
invinds=None,
diribcs=None,
return_vp=False,
ppin=-1,
N=None,
nu=None,
vel_pcrd_stps=10,
vel_pcrd_tol=1e-4,
vel_nwtn_stps=20,
vel_nwtn_tol=5e-15,
clearprvdata=False,
vel_start_nwtn=None,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
save_intermediate_steps=False,
vfileprfx='',
pfileprfx='',
**kw):
"""
Solution of the steady state nonlinear NSE Problem
using Newton's scheme. If no starting value is provided, the iteration
is started with the steady state Stokes solution.
Parameters
----------
A : (N,N) sparse matrix
stiffness matrix aka discrete Laplacian, note the sign!
M : (N,N) sparse matrix
mass matrix
J : (M,N) sparse matrix
discrete divergence operator
JT : (N,M) sparse matrix, optional
discrete gradient operator, set to J.T if not provided
fv, fp : (N,1), (M,1) ndarrays
right hand sides restricted via removing the boundary nodes in the
momentum and the pressure freedom in the continuity equation
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
return_vp : boolean, optional
whether to return also the pressure, defaults to `False`
vel_pcrd_stps : int, optional
Number of Picard iterations when computing a starting value for the
Newton scheme, cf. Elman, Silvester, Wathen: *FEM and fast iterative
solvers*, 2005, defaults to `100`
vel_pcrd_tol : real, optional
tolerance for the size of the Picard update, defaults to `1e-4`
vel_nwtn_stps : int, optional
Number of Newton iterations, defaults to `20`
vel_nwtn_tol : real, optional
tolerance for the size of the Newton update, defaults to `5e-15`
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if get_datastring is None:
get_datastring = get_datastr_snu
if JT is None:
JT = J.T
NV = J.shape[1]
#
# Compute or load the uncontrolled steady state Navier-Stokes solution
#
norm_nwtnupd_list = []
vel_newtk, norm_nwtnupd = 0, 1
# a dict to be passed to the get_datastring function
datastrdict = dict(time=None,
meshp=N,
nu=nu,
Nts=None,
data_prfx=data_prfx)
if clearprvdata:
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '*__vel*'):
os.remove(fname)
try:
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = dou.load_npa(cdatstr + '__norm_nwtnupd')
vel_k = dou.load_npa(cdatstr + '__vel')
norm_nwtnupd_list.append(norm_nwtnupd)
print('found vel files')
print('norm of last Nwtn update: {0}'.format(norm_nwtnupd))
print('... loaded from ' + cdatstr)
if np.atleast_1d(norm_nwtnupd)[0] is None:
norm_nwtnupd = None
pass # nothing useful found
elif norm_nwtnupd < vel_nwtn_tol:
if not return_vp:
return vel_k, norm_nwtnupd_list
else:
pfv = get_pfromv(v=vel_k[:NV, :],
V=V,
M=M,
A=A,
J=J,
fv=fv,
invinds=invinds,
diribcs=diribcs)
return (np.vstack([vel_k, pfv]), norm_nwtnupd_list)
except IOError:
print('no old velocity data found')
norm_nwtnupd = None
if paraviewoutput:
cdatstr = get_datastring(**datastrdict)
vfile = dolfin.File(vfileprfx + '__steadystates.pvd')
pfile = dolfin.File(pfileprfx + '__steadystates.pvd')
prvoutdict = dict(V=V,
Q=Q,
vfile=vfile,
pfile=pfile,
invinds=invinds,
diribcs=diribcs,
ppin=ppin,
vp=None,
t=None,
writeoutput=True)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' here
NV = A.shape[0]
if vel_start_nwtn is None:
vp_stokes = lau.solve_sadpnt_smw(amat=A,
jmat=J,
jmatT=JT,
rhsv=fv,
rhsp=fp)
vp_stokes[NV:] = -vp_stokes[NV:]
# pressure was flipped for symmetry
# save the data
cdatstr = get_datastring(**datastrdict)
dou.save_npa(vp_stokes[:NV, ], fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_stokes))
dou.output_paraview(**prvoutdict)
# Stokes solution as starting value
vp_k = vp_stokes
vel_k = vp_stokes[:NV, ]
else:
vel_k = vel_start_nwtn
# Picard iterations for a good starting value for Newton
for k in range(vel_pcrd_stps):
(convc_mat, rhs_con, rhsv_conbc) = get_v_conv_conts(prev_v=vel_k,
invinds=invinds,
V=V,
diribcs=diribcs,
Picard=True)
vp_k = lau.solve_sadpnt_smw(amat=A + convc_mat,
jmat=J,
jmatT=JT,
rhsv=fv + rhs_con + rhsv_conbc,
rhsp=fp)
normpicupd = np.sqrt(m_innerproduct(M, vel_k - vp_k[:NV, :]))[0]
print('Picard iteration: {0} -- norm of update: {1}'.format(
k + 1, normpicupd))
vel_k = vp_k[:NV, ]
vp_k[NV:] = -vp_k[NV:]
# pressure was flipped for symmetry
if normpicupd < vel_pcrd_tol:
break
# Newton iteration
while (vel_newtk < vel_nwtn_stps
and (norm_nwtnupd is None or norm_nwtnupd > vel_nwtn_tol
or norm_nwtnupd == np.array(None))):
vel_newtk += 1
cdatstr = get_datastring(**datastrdict)
(convc_mat, rhs_con, rhsv_conbc) = get_v_conv_conts(vel_k,
invinds=invinds,
V=V,
diribcs=diribcs)
vp_k = lau.solve_sadpnt_smw(amat=A + convc_mat,
jmat=J,
jmatT=JT,
rhsv=fv + rhs_con + rhsv_conbc,
rhsp=fp)
norm_nwtnupd = np.sqrt(m_innerproduct(M, vel_k - vp_k[:NV, :]))[0]
vel_k = vp_k[:NV, ]
vp_k[NV:] = -vp_k[NV:]
# pressure was flipped for symmetry
print('Steady State NSE: Newton iteration: {0} -- norm of update: {1}'.
format(vel_newtk, norm_nwtnupd))
dou.save_npa(vel_k, fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_k))
dou.output_paraview(**prvoutdict)
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
dou.output_paraview(**prvoutdict)
# savetomatlab = True
# if savetomatlab:
# export_mats_to_matlab(E=None, A=None, matfname='matexport')
if return_vp:
return vp_k, norm_nwtnupd_list
else:
return vel_k, norm_nwtnupd_list
def test_qbdae_ass(problemname='cylinderwake', N=1, Re=None, nu=3e-2,
t0=0.0, tE=1.0, Nts=100, use_saved_mats=None):
trange = np.linspace(t0, tE, Nts+1)
DT = (tE-t0)/Nts
rdir = 'results/'
ddir = 'data/'
if use_saved_mats is None:
femp, stokesmatsc, rhsd_vfrc, rhsd_stbc = \
dns.problem_setups.get_sysmats(problem=problemname, N=N, Re=Re)
invinds = femp['invinds']
A, J, M = stokesmatsc['A'], stokesmatsc['J'], stokesmatsc['M']
L = 0*A
fvc, fpc = rhsd_vfrc['fvc'], rhsd_vfrc['fpr']
fv_stbc, fp_stbc = rhsd_stbc['fv'], rhsd_stbc['fp']
hstr = ddir + problemname + '_N{0}_hmat'.format(N)
try:
hmat = dou.load_spa(hstr)
print('loaded `hmat`')
except IOError:
print('assembling hmat ...')
hmat = dnsts.ass_convmat_asmatquad(W=femp['V'], invindsw=invinds)
dou.save_spa(hmat, hstr)
invinds = femp['invinds']
NV, NP = invinds.shape[0], J.shape[0]
zerv = np.zeros((NV, 1))
bc_conv, bc_rhs_conv, rhsbc_convbc = \
snu.get_v_conv_conts(prev_v=zerv, V=femp['V'], invinds=invinds,
diribcs=femp['diribcs'], Picard=False)
fp = fp_stbc + fpc
fv = fv_stbc + fvc - bc_rhs_conv
if linnsesol:
vp_nse, _ = snu.\
solve_steadystate_nse(A=A, J=J, JT=None, M=M,
fv=fv_stbc + fvc,
fp=fp_stbc + fpc,
V=femp['V'], Q=femp['Q'],
invinds=invinds,
diribcs=femp['diribcs'],
return_vp=False, ppin=-1,
N=N, nu=nu,
clearprvdata=False)
old_v = vp_nse[:NV]
else:
import sadptprj_riclyap_adi.lin_alg_utils as lau
# Stokes solution as initial value
vp_stokes = lau.solve_sadpnt_smw(amat=A, jmat=J,
rhsv=fv_stbc + fvc,
rhsp=fp_stbc + fpc)
old_v = vp_stokes[:NV]
sysmat = sps.vstack([sps.hstack([M+DT*(A+bc_conv), J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])])
if use_saved_mats is not None:
# if saved as in ../get_exp_mats
import scipy.io
mats = scipy.io.loadmat(use_saved_mats)
A = - mats['A']
L = - mats['L']
Re = mats['Re']
N = A.shape[0]
M = mats['M']
J = mats['J']
hmat = -mats['H']
fv = mats['fv']
fp = mats['fp']
NV, NP = fv.shape[0], fp.shape[0]
old_v = mats['ss_stokes']
sysmat = sps.vstack([sps.hstack([M+DT*A, J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])])
if compevs:
import matplotlib.pyplot as plt
import scipy.linalg as spla
hlstr = ddir + problemname + '_N{0}_Re{1}Nse{2}_hlmat'.\
format(N, Re, linnsesol)
HL = linearzd_quadterm(hmat, old_v, hlstr=hlstr)
print(HL.shape)
asysmat = sps.vstack([sps.hstack([-(A-L+HL), J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])])
msysmat = sps.vstack([sps.hstack([M, sps.csc_matrix((NV, NP))]),
sps.hstack([sps.csc_matrix((NP, NV)),
sps.csc_matrix((NP, NP))])])
levstr = ddir + problemname + '_N{0}Re{1}Nse{2}_levs'.\
format(N, Re, linnsesol)
try:
levs = dou.load_npa(levstr)
if debug:
raise IOError()
print('loaded the eigenvalues of the linearized system')
except IOError:
print('computing the eigenvalues of the linearized system')
A = asysmat.todense()
M = msysmat.todense()
levs = spla.eigvals(A, M, overwrite_a=True, check_finite=False)
dou.save_npa(levs, levstr)
plt.figure(1)
# plt.xlim((-25, 15))
# plt.ylim((-50, 50))
plt.plot(np.real(levs), np.imag(levs), '+')
plt.show(block=False)
if timeint:
print('computing LU once...')
sysmati = spsla.factorized(sysmat)
vfile = dolfin.File(rdir + problemname + 'qdae__vel.pvd')
pfile = dolfin.File(rdir + problemname + 'qdae__p.pvd')
prvoutdict = dict(V=femp['V'], Q=femp['Q'], vfile=vfile, pfile=pfile,
invinds=invinds, diribcs=femp['diribcs'],
vp=None, t=None, writeoutput=True)
print('doing the time loop...')
for t in trange:
crhsv = M*old_v + DT*(fv - hmat*np.kron(old_v, old_v))
crhs = np.vstack([crhsv, fp])
vp_new = np.atleast_2d(sysmati(crhs.flatten())).T
prvoutdict.update(dict(vp=vp_new, t=t))
dou.output_paraview(**prvoutdict)
old_v = vp_new[:NV]
print(t, np.linalg.norm(old_v))
def solve_nse(
A=None,
M=None,
J=None,
JT=None,
fv=None,
fp=None,
fvc=None,
fpc=None, # TODO: this is to catch deprecated calls
fv_tmdp=None,
fv_tmdp_params={},
fv_tmdp_memory=None,
iniv=None,
lin_vel_point=None,
stokes_flow=False,
trange=None,
t0=None,
tE=None,
Nts=None,
V=None,
Q=None,
invinds=None,
diribcs=None,
output_includes_bcs=False,
N=None,
nu=None,
ppin=-1,
closed_loop=False,
static_feedback=False,
feedbackthroughdict=None,
return_vp=False,
tb_mat=None,
c_mat=None,
vel_nwtn_stps=20,
vel_nwtn_tol=5e-15,
nsects=1,
loc_nwtn_tol=5e-15,
loc_pcrd_stps=True,
addfullsweep=False,
vel_pcrd_stps=4,
krylov=None,
krpslvprms={},
krplsprms={},
clearprvdata=False,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
vfileprfx='',
pfileprfx='',
return_dictofvelstrs=False,
return_dictofpstrs=False,
dictkeysstr=False,
comp_nonl_semexp=False,
return_as_list=False,
verbose=True,
start_ssstokes=False,
**kw):
"""
solution of the time-dependent nonlinear Navier-Stokes equation
.. math::
M\\dot v + Av + N(v)v + J^Tp = f \n
Jv =g
using a Newton scheme in function space, i.e. given :math:`v_k`,
we solve for the update like
.. math::
M\\dot v + Av + N(v_k)v + N(v)v_k + J^Tp = N(v_k)v_k + f,
and trapezoidal rule in time. To solve an *Oseen* system (linearization
about a steady state) or a *Stokes* system, set the number of Newton
steps to one and provide a linearization point and an initial value.
Parameters
----------
lin_vel_point : dictionary, optional
contains the linearization point for the first Newton iteration
* Steady State: {{`None`: 'path_to_nparray'}, {'None': nparray}}
* Newton: {`t`: 'path_to_nparray'}
defaults to `None`
dictkeysstr : boolean, optional
whether the `keys` of the result dictionaries are strings instead \
of floats, defaults to `False`
fv_tmdp : callable f(t, v, dict), optional
time-dependent part of the right-hand side, set to zero if None
fv_tmdp_params : dictionary, optional
dictionary of parameters to be passed to `fv_tmdp`, defaults to `{}`
fv_tmdp_memory : dictionary, optional
memory of the function
output_includes_bcs : boolean, optional
whether append the boundary nodes to the computed and stored \
velocities, defaults to `False`
krylov : {None, 'gmres'}, optional
whether or not to use an iterative solver, defaults to `None`
krpslvprms : dictionary, optional
to specify parameters of the linear solver for use in Krypy, e.g.,
* initial guess
* tolerance
* number of iterations
defaults to `None`
krplsprms : dictionary, optional
parameters to define the linear system like
* preconditioner
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
stokes_flow : boolean, optional
whether to consider the Stokes linearization, defaults to `False`
start_ssstokes : boolean, optional
for your convenience, compute and use the steady state stokes solution
as initial value, defaults to `False`
nsects: int, optional
in how many segments the trange is split up. (The newton iteration
will be confined to the segments and, probably, converge faster than
the global iteration), defaults to `1`
loc_nwtn_tol: float, optional
tolerance for the newton iteration on the segments,
defaults to `1e-15`
loc_pcrd_stps: boolean, optional
whether to init with `vel_pcrd_stps` Picard steps on every section,
if `False`, Picard iterations are performed only on the first section,
defaults to `True`
addfullsweep: boolean, optional
whether to compute the newton iteration on the full `trange`,
useful to check and for the plots, defaults to `False`
Returns
-------
dictofvelstrs : dictionary, on demand
dictionary with time `t` as keys and path to velocity files as values
dictofpstrs : dictionary, on demand
dictionary with time `t` as keys and path to pressure files as values
vellist : list, on demand
list of the velocity solutions
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if fvc is not None or fpc is not None: # TODO: this is for catching calls
raise UserWarning('deprecated use of `rhsd_vfrc`, use only `fv`, `fp`')
if get_datastring is None:
get_datastring = get_datastr_snu
if paraviewoutput:
prvoutdict = dict(V=V,
Q=Q,
invinds=invinds,
diribcs=diribcs,
vp=None,
t=None,
writeoutput=True,
ppin=ppin)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' here
if trange is None:
trange = np.linspace(t0, tE, Nts + 1)
if comp_nonl_semexp and lin_vel_point is not None:
raise UserWarning('I am not sure what you want! ' +
'set either `lin_vel_point=None` ' +
'or `comp_nonl_semexp=False`! \n' +
'as it is, I will compute a linear case')
if return_dictofpstrs:
gpfvd = dict(V=V,
M=M,
A=A,
J=J,
fv=fv,
fp=fp,
diribcs=diribcs,
invinds=invinds)
NV, NP = A.shape[0], J.shape[0]
if fv_tmdp is None:
def fv_tmdp(time=None, curvel=None, **kw):
return np.zeros((NV, 1)), None
if iniv is None:
if start_ssstokes:
# Stokes solution as starting value
(fv_tmdp_cont, fv_tmdp_memory) = fv_tmdp(time=0, **fv_tmdp_params)
vp_stokes =\
lau.solve_sadpnt_smw(amat=A, jmat=J, jmatT=JT,
rhsv=fv + fv_tmdp_cont,
krylov=krylov, krpslvprms=krpslvprms,
krplsprms=krplsprms, rhsp=fp)
iniv = vp_stokes[:NV]
else:
raise ValueError('No initial value given')
datastrdict = dict(time=None,
meshp=N,
nu=nu,
Nts=trange.size - 1,
data_prfx=data_prfx)
if return_as_list:
clearprvdata = True # we want the results at hand
if clearprvdata:
datastrdict['time'] = '*'
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '__vel*'):
os.remove(fname)
for fname in glob.glob(cdatstr + '__p*'):
os.remove(fname)
def _atdct(cdict, t, thing):
if dictkeysstr:
cdict.update({'{0}'.format(t): thing})
else:
cdict.update({t: thing})
def _gfdct(cdict, t):
if dictkeysstr:
return cdict['{0}'.format(t)]
else:
return cdict[t]
if stokes_flow:
vel_nwtn_stps = 1
vel_pcrd_stps = 0
print('Stokes Flow!')
elif lin_vel_point is None:
comp_nonl_semexp_inig = True
if not comp_nonl_semexp:
print(('No linearization point given - explicit' +
' treatment of the nonlinearity in the first Iteration'))
else:
cur_linvel_point = lin_vel_point
comp_nonl_semexp_inig = False
newtk, norm_nwtnupd = 0, 1
# check for previously computed velocities
if lin_vel_point is None and not stokes_flow:
try:
datastrdict.update(dict(time=trange[-1]))
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = (dou.load_npa(cdatstr + '__norm_nwtnupd')).flatten()
try:
if norm_nwtnupd[0] is None:
norm_nwtnupd = 1.
except IndexError:
norm_nwtnupd = 1.
dou.load_npa(cdatstr + '__vel')
print('found vel files')
print('norm of last Nwtn update: {0}'.format(norm_nwtnupd))
print('... loaded from ' + cdatstr)
if norm_nwtnupd < vel_nwtn_tol and not return_dictofvelstrs:
return
elif norm_nwtnupd < vel_nwtn_tol:
# looks like converged -- check if all values are there
# t0:
datastrdict.update(dict(time=trange[0]))
cdatstr = get_datastring(**datastrdict)
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
dictofpstrs = {}
# try:
# p_old = dou.load_npa(cdatstr + '__p')
# dictofpstrs = {}
# _atdct(dictofpstrs, trange[0], cdatstr+'__p')
# except:
# p_old = get_pfromv(v=v_old, **gpfvd)
# dou.save_npa(p_old, fstring=cdatstr + '__p')
# _atdct(dictofpstrs, trange[0], cdatstr+'__p')
for t in trange:
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
# test if the vels are there
v_old = dou.load_npa(cdatstr + '__vel')
# update the dict
_atdct(dictofvelstrs, t, cdatstr + '__vel')
try:
p_old = dou.load_npa(cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
except:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
comp_nonl_semexp = False
except IOError:
norm_nwtnupd = 2
print('no old velocity data found')
def _append_bcs_ornot(vvec):
if output_includes_bcs: # make the switch here for better readibility
vwbcs = dts.append_bcs_vec(vvec,
vdim=V.dim(),
invinds=invinds,
diribcs=diribcs)
return vwbcs
else:
return vvec
def _get_mats_rhs_ts(mmat=None,
dt=None,
var_c=None,
coeffmat_c=None,
coeffmat_n=None,
fv_c=None,
fv_n=None,
umat_c=None,
vmat_c=None,
umat_n=None,
vmat_n=None,
impeul=False):
""" to be tweaked for different int schemes
"""
solvmat = M + 0.5 * dt * coeffmat_n
rhs = M * var_c + 0.5 * dt * (fv_n + fv_c - coeffmat_c * var_c)
if umat_n is not None:
matvec = lau.mm_dnssps
umat = 0.5 * dt * umat_n
vmat = vmat_n
# TODO: do we really need a PLUS here??'
rhs = rhs + 0.5 * dt * matvec(umat_c, matvec(vmat_c, var_c))
else:
umat, vmat = umat_n, vmat_n
return solvmat, rhs, umat, vmat
v_old = iniv # start vector for time integration in every Newtonit
datastrdict['time'] = trange[0]
cdatstr = get_datastring(**datastrdict)
dou.save_npa(_append_bcs_ornot(v_old), fstring=cdatstr + '__vel')
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
dictofpstrs = {}
_atdct(dictofpstrs, trange[0], cdatstr + '__p')
else:
p_old = None
if return_as_list:
vellist = []
vellist.append(_append_bcs_ornot(v_old))
lensect = np.int(np.floor(trange.size / nsects))
loctrngs = []
for k in np.arange(nsects - 1):
loctrngs.append(trange[k * lensect:(k + 1) * lensect + 1])
loctrngs.append(trange[(nsects - 1) * lensect:])
if addfullsweep:
loctrngs.append(trange)
realiniv = np.copy(iniv)
if nsects == 1:
loc_nwtn_tol = vel_nwtn_tol
addfullsweep = False
loctrngs = [trange]
if loc_pcrd_stps:
vel_loc_pcrd_steps = vel_pcrd_stps
for loctrng in loctrngs:
while (newtk < vel_nwtn_stps and norm_nwtnupd > loc_nwtn_tol):
print('solve the NSE on the interval [{0}, {1}]'.format(
loctrng[0], loctrng[-1]))
if stokes_flow:
newtk = vel_nwtn_stps
elif comp_nonl_semexp_inig and not comp_nonl_semexp:
pcrd_anyone = False
print('explicit treatment of nonl. for initial guess')
elif vel_pcrd_stps > 0 and not comp_nonl_semexp:
vel_pcrd_stps -= 1
pcrd_anyone = True
print('Picard iterations for initial value -- {0} left'.format(
vel_pcrd_stps))
elif comp_nonl_semexp:
pcrd_anyone = False
newtk = vel_nwtn_stps
print('No Newton iterations - explicit treatment' +
'of the nonlinerity')
else:
pcrd_anyone = False
newtk += 1
print('Computing Newton Iteration {0}'.format(newtk))
v_old = iniv # start vector for time integration in every Newtonit
try:
if krpslvprms['krylovini'] == 'old':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
elif krpslvprms['krylovini'] == 'upd':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
vp_new = vp_old
cts_old = loctrng[1] - loctrng[0]
except (TypeError, KeyError):
pass # no inival for krylov solver required
vfile = dolfin.File(vfileprfx + '__timestep.pvd')
pfile = dolfin.File(pfileprfx + '__timestep.pvd')
prvoutdict.update(
dict(vp=None,
vc=iniv,
pc=p_old,
t=loctrng[0],
pfile=pfile,
vfile=vfile))
dou.output_paraview(**prvoutdict)
# ## current values_c for application of trap rule
if stokes_flow:
convc_mat_c = sps.csr_matrix((NV, NV))
rhs_con_c, rhsv_conbc_c = np.zeros((NV, 1)), np.zeros((NV, 1))
else:
if comp_nonl_semexp or comp_nonl_semexp_inig:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(
_gfdct(cur_linvel_point, loctrng[0]))
except KeyError:
try:
prev_v = dou.load_npa(
_gfdct(cur_linvel_point, None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_c, rhs_con_c, rhsv_conbc_c = \
get_v_conv_conts(prev_v=iniv, invinds=invinds,
V=V, diribcs=diribcs, Picard=pcrd_anyone)
(fv_tmdp_cont, fv_tmdp_memory) = fv_tmdp(time=0,
curvel=v_old,
memory=fv_tmdp_memory,
**fv_tmdp_params)
fvn_c = fv + rhsv_conbc_c + rhs_con_c + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_c = dou.load_npa(feedbackthroughdict[None]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[None]['w'])
# print '\nnorm of feedback: ', np.linalg.norm(mtxtb_c)
else:
mtxtb_c = dou.load_npa(feedbackthroughdict[0]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[0]['w'])
fvn_c = fvn_c + tb_mat * (tb_mat.T * w_c)
vmat_c = mtxtb_c.T
try:
umat_c = np.array(tb_mat.todense())
except AttributeError:
umat_c = tb_mat
else:
vmat_c = None
umat_c = None
norm_nwtnupd = 0
if verbose:
print('time to go')
for tk, t in enumerate(loctrng[1:]):
cts = t - loctrng[tk]
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
if verbose:
sys.stdout.write("\rEnd: {1} -- now: {0:f}".format(
t, loctrng[-1]))
sys.stdout.flush()
# prv_datastrdict = copy.deepcopy(datastrdict)
# coeffs and rhs at next time instance
if stokes_flow:
convc_mat_n = sps.csr_matrix((NV, NV))
rhs_con_n = np.zeros((NV, 1))
rhsv_conbc_n = np.zeros((NV, 1))
else:
if comp_nonl_semexp or comp_nonl_semexp_inig:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point, t))
except KeyError:
try:
prev_v = dou.load_npa(
_gfdct(cur_linvel_point, None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_n, rhs_con_n, rhsv_conbc_n = \
get_v_conv_conts(prev_v=prev_v, invinds=invinds, V=V,
diribcs=diribcs, Picard=pcrd_anyone)
(fv_tmdp_cont, fv_tmdp_memory) = fv_tmdp(time=t,
curvel=v_old,
memory=fv_tmdp_memory,
**fv_tmdp_params)
fvn_n = fv + rhsv_conbc_n + rhs_con_n + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_n = dou.\
load_npa(feedbackthroughdict[None]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[None]['w'])
# fb = np.dot(tb_mat*mtxtb_n.T, v_old)
# print '\nnorm of feedback: ', np.linalg.norm(fb)
# print '\nnorm of v_old: ', np.linalg.norm(v_old)
else:
mtxtb_n = dou.load_npa(feedbackthroughdict[t]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[t]['w'])
fvn_n = fvn_n + tb_mat * (tb_mat.T * w_n)
vmat_n = mtxtb_n.T
try:
umat_n = np.array(tb_mat.todense())
except AttributeError:
umat_n = tb_mat
else:
vmat_n = None
umat_n = None
(solvmat, rhsv, umat,
vmat) = _get_mats_rhs_ts(mmat=M,
dt=cts,
var_c=v_old,
coeffmat_c=A + convc_mat_c,
coeffmat_n=A + convc_mat_n,
fv_c=fvn_c,
fv_n=fvn_n,
umat_c=umat_c,
vmat_c=vmat_c,
umat_n=umat_n,
vmat_n=vmat_n)
try:
if krpslvprms['krylovini'] == 'old':
krpslvprms['x0'] = vp_old
elif krpslvprms['krylovini'] == 'upd':
vp_oldold = vp_old
vp_old = vp_new
krpslvprms['x0'] = vp_old + \
cts*(vp_old - vp_oldold)/cts_old
cts_old = cts
except (TypeError, KeyError):
pass # no inival for krylov solver required
vp_new = lau.solve_sadpnt_smw(amat=solvmat,
jmat=J,
jmatT=JT,
rhsv=rhsv,
rhsp=fp,
krylov=krylov,
krpslvprms=krpslvprms,
krplsprms=krplsprms,
umat=umat,
vmat=vmat)
v_old = vp_new[:NV, ]
(umat_c, vmat_c, fvn_c,
convc_mat_c) = umat_n, vmat_n, fvn_n, convc_mat_n
dou.save_npa(_append_bcs_ornot(v_old),
fstring=cdatstr + '__vel')
_atdct(dictofvelstrs, t, cdatstr + '__vel')
p_new = -1 / cts * vp_new[NV:, ]
# p was flipped and scaled for symmetry
if return_dictofpstrs:
dou.save_npa(p_new, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_as_list:
vellist.append(_append_bcs_ornot(v_old))
prvoutdict.update(dict(vc=v_old, pc=p_new, t=t))
dou.output_paraview(**prvoutdict)
# integrate the Newton error
if stokes_flow or comp_nonl_semexp:
norm_nwtnupd = None
elif comp_nonl_semexp_inig:
norm_nwtnupd = 1.
else:
if len(prev_v) > len(invinds):
prev_v = prev_v[invinds, :]
addtonwtnupd = cts * m_innerproduct(M, v_old - prev_v)
norm_nwtnupd += np.float(addtonwtnupd.flatten()[0])
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
print('\nnorm of current Newton update: {}'.format(norm_nwtnupd))
# print('\nsaved `norm_nwtnupd(={0})'.format(norm_nwtnupd) +
# ' to ' + cdatstr)
comp_nonl_semexp = False
comp_nonl_semexp_inig = False
cur_linvel_point = dictofvelstrs
iniv = v_old
if not comp_nonl_semexp:
comp_nonl_semexp_inig = True
if addfullsweep and loctrng is loctrngs[-2]:
comp_nonl_semexp_inig = False
iniv = realiniv
loc_nwtn_tol = vel_nwtn_tol
elif loc_pcrd_stps:
vel_pcrd_stps = vel_loc_pcrd_steps
norm_nwtnupd = 1.
newtk = 0
if return_dictofvelstrs:
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
elif return_as_list:
return vellist
else:
return
def test_qbdae_ass(problemname='cylinderwake', N=1, Re=4e2, nu=3e-2,
t0=0.0, tE=1.0, Nts=100, use_saved_mats=None):
trange = np.linspace(t0, tE, Nts+1)
DT = (tE-t0)/Nts
rdir = 'results/'
femp, stokesmatsc, rhsd_vfrc, rhsd_stbc, \
data_prfx, ddir, proutdir = \
dns.problem_setups.get_sysmats(problem=problemname, N=N, Re=Re)
invinds = femp['invinds']
if use_saved_mats is None:
A, J, M = stokesmatsc['A'], stokesmatsc['J'], stokesmatsc['M']
fvc, fpc = rhsd_vfrc['fvc'], rhsd_vfrc['fpr']
fv_stbc, fp_stbc = rhsd_stbc['fv'], rhsd_stbc['fp']
hstr = ddir + problemname + '_N{0}_hmat'.format(N)
try:
hmat = dou.load_spa(hstr)
print 'loaded `hmat`'
except IOError:
print 'assembling hmat ...'
hmat = dnsts.ass_convmat_asmatquad(W=femp['V'], invindsw=invinds)
dou.save_spa(hmat, hstr)
invinds = femp['invinds']
NV, NP = invinds.shape[0], J.shape[0]
zerv = np.zeros((NV, 1))
bc_conv, bc_rhs_conv, rhsbc_convbc = \
snu.get_v_conv_conts(prev_v=zerv, V=femp['V'], invinds=invinds,
diribcs=femp['diribcs'], Picard=False)
fp = fp_stbc + fpc
fv = fv_stbc + fvc - bc_rhs_conv
# Stokes solution as initial value
vp_stokes = lau.solve_sadpnt_smw(amat=A, jmat=J,
rhsv=fv_stbc + fvc,
rhsp=fp_stbc + fpc)
old_v = vp_stokes[:NV]
sysmat = sps.vstack([sps.hstack([M+DT*(A+bc_conv), J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])])
# the observation
if problemname == 'cylinderwake':
podcoo = dict(xmin=0.6,
xmax=0.64,
ymin=0.18,
ymax=0.22)
elif problemname == 'drivencavity':
podcoo = dict(xmin=0.45,
xmax=0.55,
ymin=0.7,
ymax=0.8)
else:
podcoo = femp['odcoo']
pcmat = cou.get_pavrg_onsubd(odcoo=podcoo, Q=femp['Q'])
if use_saved_mats is not None:
# if saved as in ../get_exp_mats
import scipy.io
mats = scipy.io.loadmat(use_saved_mats)
A = - mats['A']
M = mats['M']
J = mats['J']
hmat = -mats['H']
fv = mats['fv']
fp = mats['fp']
NV, NP = fv.shape[0], fp.shape[0]
old_v = mats['ss_stokes']
sysmat = sps.vstack([sps.hstack([M+DT*A, J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])])
pcmat = mats['Cp']
print 'computing LU once...'
sysmati = spsla.factorized(sysmat)
vfile = dolfin.File(rdir + problemname + 'qdae__vel.pvd')
pfile = dolfin.File(rdir + problemname + 'qdae__p.pvd')
prvoutdict = dict(V=femp['V'], Q=femp['Q'], vfile=vfile, pfile=pfile,
invinds=invinds, diribcs=femp['diribcs'],
vp=None, t=None, writeoutput=True)
print 'doing the time loop...'
poutlist = []
for t in trange:
# conv_mat, rhs_conv, rhsbc_conv = \
# snu.get_v_conv_conts(prev_v=old_v, V=femp['V'], invinds=invinds,
# diribcs=femp['diribcs'], Picard=False)
# crhsv = M*old_v + DT*(fv_stbc + fvc + rhs_conv + rhsbc_conv
# - conv_mat*old_v)
# raise Warning('TODO: debug')
crhsv = M*old_v + DT*(fv - hmat*np.kron(old_v, old_v))
crhs = np.vstack([crhsv, fp])
vp_new = np.atleast_2d(sysmati(crhs.flatten())).T
# vp_new = lau.solve_sadpnt_smw(amat=M+DT*(A+0*conv_mat), jmat=J,
# rhsv=crhsv,
# rhsp=fp_stbc + fpc)
vp_new[NV:] = pcmat.T # *vp_new[NV:]
prvoutdict.update(dict(vp=vp_new, t=t))
dou.output_paraview(**prvoutdict)
old_v = vp_new[:NV]
p = vp_new[NV:]
poutlist.append(np.dot(pcmat, p)[0][0])
print t, np.linalg.norm(old_v)
dou.plot_prs_outp(outsig=poutlist, tmesh=trange)
def solve_nse(A=None, M=None, J=None, JT=None,
fv=None, fp=None,
fvc=None, fpc=None, # TODO: this is to catch deprecated calls
fv_tmdp=None, fv_tmdp_params={},
fv_tmdp_memory=None,
iniv=None, lin_vel_point=None,
stokes_flow=False,
trange=None,
t0=None, tE=None, Nts=None,
V=None, Q=None, invinds=None, diribcs=None,
dbcinds=None, dbcvals=None,
output_includes_bcs=False,
N=None, nu=None,
ppin=-1,
closed_loop=False, static_feedback=False,
feedbackthroughdict=None,
return_vp=False,
tb_mat=None, cv_mat=None,
vel_nwtn_stps=20, vel_nwtn_tol=5e-15,
nsects=1, loc_nwtn_tol=5e-15, loc_pcrd_stps=True,
addfullsweep=False,
vel_pcrd_stps=4,
krylov=None, krpslvprms={}, krplsprms={},
clearprvdata=False,
useolddata=False,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
plttrange=None,
vfileprfx='', pfileprfx='',
return_dictofvelstrs=False,
return_dictofpstrs=False,
dictkeysstr=False,
treat_nonl_explct=False,
return_as_list=False,
verbose=True,
start_ssstokes=False,
**kw):
"""
solution of the time-dependent nonlinear Navier-Stokes equation
.. math::
M\\dot v + Av + N(v)v + J^Tp = f \n
Jv =g
using a Newton scheme in function space, i.e. given :math:`v_k`,
we solve for the update like
.. math::
M\\dot v + Av + N(v_k)v + N(v)v_k + J^Tp = N(v_k)v_k + f,
and trapezoidal rule in time. To solve an *Oseen* system (linearization
about a steady state) or a *Stokes* system, set the number of Newton
steps to one and provide a linearization point and an initial value.
Parameters
----------
lin_vel_point : dictionary, optional
contains the linearization point for the first Newton iteration
* Steady State: {{`None`: 'path_to_nparray'}, {'None': nparray}}
* Newton: {`t`: 'path_to_nparray'}
defaults to `None`
dictkeysstr : boolean, optional
whether the `keys` of the result dictionaries are strings instead \
of floats, defaults to `False`
fv_tmdp : callable f(t, v, dict), optional
time-dependent part of the right-hand side, set to zero if None
fv_tmdp_params : dictionary, optional
dictionary of parameters to be passed to `fv_tmdp`, defaults to `{}`
fv_tmdp_memory : dictionary, optional
memory of the function
output_includes_bcs : boolean, optional
whether append the boundary nodes to the computed and stored \
velocities, defaults to `False`
krylov : {None, 'gmres'}, optional
whether or not to use an iterative solver, defaults to `None`
krpslvprms : dictionary, optional
to specify parameters of the linear solver for use in Krypy, e.g.,
* initial guess
* tolerance
* number of iterations
defaults to `None`
krplsprms : dictionary, optional
parameters to define the linear system like
* preconditioner
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
stokes_flow : boolean, optional
whether to consider the Stokes linearization, defaults to `False`
start_ssstokes : boolean, optional
for your convenience, compute and use the steady state stokes solution
as initial value, defaults to `False`
treat_nonl_explct= string, optional
whether to treat the nonlinearity explicitly, defaults to `False`
nsects: int, optional
in how many segments the trange is split up. (The newton iteration
will be confined to the segments and, probably, converge faster than
the global iteration), defaults to `1`
loc_nwtn_tol: float, optional
tolerance for the newton iteration on the segments,
defaults to `1e-15`
loc_pcrd_stps: boolean, optional
whether to init with `vel_pcrd_stps` Picard steps on every section,
if `False`, Picard iterations are performed only on the first section,
defaults to `True`
addfullsweep: boolean, optional
whether to compute the newton iteration on the full `trange`,
useful to check and for the plots, defaults to `False`
cv_mat: (Ny, Nv) sparse array, optional
output matrix for velocity outputs, needed, e.g., for output dependent
feedback control, defaults to `None`
Returns
-------
dictofvelstrs : dictionary, on demand
dictionary with time `t` as keys and path to velocity files as values
dictofpstrs : dictionary, on demand
dictionary with time `t` as keys and path to pressure files as values
vellist : list, on demand
list of the velocity solutions
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if fvc is not None or fpc is not None: # TODO: this is for catching calls
raise UserWarning('deprecated use of `rhsd_vfrc`, use only `fv`, `fp`')
if get_datastring is None:
get_datastring = get_datastr_snu
if paraviewoutput:
prvoutdict = dict(V=V, Q=Q,
invinds=invinds, diribcs=diribcs, ppin=ppin,
vp=None, t=None,
tfilter=plttrange, writeoutput=True)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' here
if trange is None:
trange = np.linspace(t0, tE, Nts+1)
if treat_nonl_explct and lin_vel_point is not None:
raise UserWarning('cant use `lin_vel_point` ' +
'and explicit treatment of the nonlinearity')
if return_dictofpstrs:
gpfvd = dict(V=V, M=M, A=A, J=J,
fv=fv, fp=fp,
dbcinds=dbcinds, dbcvals=dbcvals,
diribcs=diribcs, invinds=invinds)
NV, NP = A.shape[0], J.shape[0]
fv = np.zeros((NV, 1)) if fv is None else fv
fp = np.zeros((NP, 1)) if fp is None else fp
if fv_tmdp is None:
def fv_tmdp(time=None, curvel=None, **kw):
return np.zeros((NV, 1)), None
if iniv is None:
if start_ssstokes:
# Stokes solution as starting value
vp_stokes =\
lau.solve_sadpnt_smw(amat=A, jmat=J, jmatT=JT,
rhsv=fv, # + fv_tmdp_cont,
krylov=krylov, krpslvprms=krpslvprms,
krplsprms=krplsprms, rhsp=fp)
iniv = vp_stokes[:NV]
else:
raise ValueError('No initial value given')
datastrdict = dict(time=None, meshp=N, nu=nu,
Nts=trange.size-1, data_prfx=data_prfx,
semiexpl=treat_nonl_explct)
if return_as_list:
clearprvdata = True # we want the results at hand
if clearprvdata:
datastrdict['time'] = '*'
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '__vel*'):
os.remove(fname)
for fname in glob.glob(cdatstr + '__p*'):
os.remove(fname)
def _atdct(cdict, t, thing):
if dictkeysstr:
cdict.update({'{0}'.format(t): thing})
else:
cdict.update({t: thing})
def _gfdct(cdict, t):
if dictkeysstr:
return cdict['{0}'.format(t)]
else:
return cdict[t]
if stokes_flow:
vel_nwtn_stps = 1
vel_pcrd_stps = 0
print('Stokes Flow!')
elif lin_vel_point is None:
comp_nonl_semexp_inig = True
if not treat_nonl_explct:
print(('No linearization point given - explicit' +
' treatment of the nonlinearity in the first Iteration'))
else:
cur_linvel_point = lin_vel_point
comp_nonl_semexp_inig = False
newtk, norm_nwtnupd = 0, 1
# check for previously computed velocities
if useolddata and lin_vel_point is None and not stokes_flow:
try:
datastrdict.update(dict(time=trange[-1]))
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = (dou.load_npa(cdatstr + '__norm_nwtnupd')).flatten()
try:
if norm_nwtnupd[0] is None:
norm_nwtnupd = 1.
except IndexError:
norm_nwtnupd = 1.
dou.load_npa(cdatstr + '__vel')
print('found vel files')
print('norm of last Nwtn update: {0}'.format(norm_nwtnupd))
print('... loaded from ' + cdatstr)
if norm_nwtnupd < vel_nwtn_tol and not return_dictofvelstrs:
return
elif norm_nwtnupd < vel_nwtn_tol or treat_nonl_explct:
# looks like converged / or semi-expl
# -- check if all values are there
# t0:
datastrdict.update(dict(time=trange[0]))
cdatstr = get_datastring(**datastrdict)
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
dictofpstrs = {}
for t in trange:
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
# test if the vels are there
v_old = dou.load_npa(cdatstr + '__vel')
# update the dict
_atdct(dictofvelstrs, t, cdatstr + '__vel')
if return_dictofpstrs:
try:
p_old = dou.load_npa(cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
except:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
# comp_nonl_semexp = False
except IOError:
norm_nwtnupd = 2
print('no old velocity data found')
def _append_bcs_ornot(vvec):
if output_includes_bcs: # make the switch here for better readibility
vwbcs = dts.append_bcs_vec(vvec, vdim=V.dim(),
invinds=invinds, diribcs=diribcs)
return vwbcs
else:
return vvec
def _get_mats_rhs_ts(mmat=None, dt=None, var_c=None,
coeffmat_c=None,
coeffmat_n=None,
fv_c=None, fv_n=None,
umat_c=None, vmat_c=None,
umat_n=None, vmat_n=None,
impeul=False):
""" to be tweaked for different int schemes
"""
solvmat = M + 0.5*dt*coeffmat_n
rhs = M*var_c + 0.5*dt*(fv_n + fv_c - coeffmat_c*var_c)
if umat_n is not None:
matvec = lau.mm_dnssps
umat = 0.5*dt*umat_n
vmat = vmat_n
# TODO: do we really need a PLUS here??'
rhs = rhs + 0.5*dt*matvec(umat_c, matvec(vmat_c, var_c))
else:
umat, vmat = umat_n, vmat_n
return solvmat, rhs, umat, vmat
v_old = iniv # start vector for time integration in every Newtonit
datastrdict['time'] = trange[0]
cdatstr = get_datastring(**datastrdict)
dou.save_npa(_append_bcs_ornot(v_old), fstring=cdatstr + '__vel')
dictofvelstrs = {}
_atdct(dictofvelstrs, trange[0], cdatstr + '__vel')
if return_dictofpstrs:
p_old = get_pfromv(v=v_old, **gpfvd)
dou.save_npa(p_old, fstring=cdatstr + '__p')
dictofpstrs = {}
_atdct(dictofpstrs, trange[0], cdatstr+'__p')
else:
p_old = None
if return_as_list:
vellist = []
vellist.append(_append_bcs_ornot(v_old))
lensect = np.int(np.floor(trange.size/nsects))
loctrngs = []
for k in np.arange(nsects-1):
loctrngs.append(trange[k*lensect: (k+1)*lensect+1])
loctrngs.append(trange[(nsects-1)*lensect:])
if addfullsweep:
loctrngs.append(trange)
realiniv = np.copy(iniv)
if nsects == 1:
loc_nwtn_tol = vel_nwtn_tol
addfullsweep = False
loctrngs = [trange]
if loc_pcrd_stps:
vel_loc_pcrd_steps = vel_pcrd_stps
for loctrng in loctrngs:
dtvec = np.array(loctrng)[1:] - np.array(loctrng)[1:]
dotdtvec = dtvec[1:] - dtvec[:-1]
uniformgrid = np.allclose(np.linalg.norm(dotdtvec), 0)
coeffmatlu = None
while (newtk < vel_nwtn_stps and norm_nwtnupd > loc_nwtn_tol):
print('solve the NSE on the interval [{0}, {1}]'.
format(loctrng[0], loctrng[-1]))
if stokes_flow:
pcrd_anyone = False
newtk = vel_nwtn_stps
elif comp_nonl_semexp_inig and not treat_nonl_explct:
pcrd_anyone = False
loc_treat_nonl_explct = True
print('explicit treatment of nonl. for initial guess!')
elif treat_nonl_explct:
pcrd_anyone = False
loc_treat_nonl_explct = True
newtk = vel_nwtn_stps
print('No Newton iterations - explicit treatment ' +
'of the nonlinearity')
if not comp_nonl_semexp_inig and not treat_nonl_explct:
if vel_pcrd_stps > 0:
vel_pcrd_stps -= 1
pcrd_anyone = True
print('Picard iterations for initial value -- {0} left'.
format(vel_pcrd_stps))
else:
pcrd_anyone = False
newtk += 1
print('Computing Newton Iteration {0}'.format(newtk))
v_old = iniv # start vector for time integration in every Newtonit
try:
if krpslvprms['krylovini'] == 'old':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
elif krpslvprms['krylovini'] == 'upd':
vp_old = np.vstack([v_old, np.zeros((NP, 1))])
vp_new = vp_old
cts_old = loctrng[1] - loctrng[0]
except (TypeError, KeyError):
pass # no inival for krylov solver required
vfile = dolfin.File(vfileprfx+'__timestep.pvd')
pfile = dolfin.File(pfileprfx+'__timestep.pvd')
prvoutdict.update(dict(vp=None, vc=iniv, pc=p_old, t=loctrng[0],
dbcinds=dbcinds, dbcvals=dbcvals,
pfile=pfile, vfile=vfile))
dou.output_paraview(**prvoutdict)
# ## current values_c for application of trap rule
if stokes_flow:
convc_mat_c = sps.csr_matrix((NV, NV))
rhs_con_c, rhsv_conbc_c = np.zeros((NV, 1)), np.zeros((NV, 1))
else:
if loc_treat_nonl_explct is not None:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point,
loctrng[0]))
except KeyError:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point,
None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_c, rhs_con_c, rhsv_conbc_c = \
get_v_conv_conts(prev_v=iniv, invinds=invinds,
semi_explicit=loc_treat_nonl_explct,
dbcinds=dbcinds, dbcvals=dbcvals,
V=V, diribcs=diribcs, Picard=pcrd_anyone)
cury = None if cv_mat is None else cv_mat.dot(v_old)
(fv_tmdp_cont,
fv_tmdp_memory) = fv_tmdp(time=0,
curvel=v_old,
cury=cury,
memory=fv_tmdp_memory,
**fv_tmdp_params)
_rhsconvc = 0. if pcrd_anyone else rhs_con_c
fvn_c = fv + rhsv_conbc_c + _rhsconvc + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_c = dou.load_npa(feedbackthroughdict[None]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[None]['w'])
else:
mtxtb_c = dou.load_npa(feedbackthroughdict[0]['mtxtb'])
w_c = dou.load_npa(feedbackthroughdict[0]['w'])
fvn_c = fvn_c + tb_mat * (tb_mat.T * w_c)
vmat_c = mtxtb_c.T
try:
umat_c = np.array(tb_mat.todense())
except AttributeError:
umat_c = tb_mat
else:
vmat_c = None
umat_c = None
norm_nwtnupd = 0
if verbose:
# define at which points of time the progress is reported
nouts = 10 # number of output points
locnts = loctrng.size # TODO: trange may be a list...
filtert = np.arange(0, locnts,
np.int(np.floor(locnts/nouts)))
loctinstances = loctrng[filtert]
loctinstances[0] = loctrng[1]
loctinstances = loctinstances.tolist()
print('doing the time integration...')
for tk, t in enumerate(loctrng[1:]):
cts = t - loctrng[tk]
datastrdict.update(dict(time=t))
cdatstr = get_datastring(**datastrdict)
try:
if verbose and t == loctinstances[0]:
curtinst = loctinstances.pop(0)
# print("runtime: {0} -- t: {1} -- tE: {2:f}".
# format(time.clock(), curtinst, loctrng[-1]))
print("runtime: {0:.1f} - t/tE: {1:.2f} - t: {2:.4f}".
format(time.clock(), curtinst/loctrng[-1],
curtinst))
except IndexError:
pass # if something goes wrong, don't stop
# coeffs and rhs at next time instance
if stokes_flow:
convc_mat_n = sps.csr_matrix((NV, NV))
rhs_con_n = np.zeros((NV, 1))
rhsv_conbc_n = np.zeros((NV, 1))
else:
if loc_treat_nonl_explct:
prev_v = v_old
else:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point, t))
except KeyError:
try:
prev_v = dou.load_npa(_gfdct(cur_linvel_point,
None))
except TypeError:
prev_v = cur_linvel_point[None]
convc_mat_n, rhs_con_n, rhsv_conbc_n = \
get_v_conv_conts(prev_v=prev_v, invinds=invinds, V=V,
semi_explicit=loc_treat_nonl_explct,
dbcinds=dbcinds, dbcvals=dbcvals,
diribcs=diribcs, Picard=pcrd_anyone)
cury = None if cv_mat is None else cv_mat.dot(v_old)
(fv_tmdp_cont,
fv_tmdp_memory) = fv_tmdp(time=t,
curvel=v_old,
cury=cury,
memory=fv_tmdp_memory,
**fv_tmdp_params)
_rhsconvn = 0. if pcrd_anyone else rhs_con_n
fvn_n = fv + rhsv_conbc_n + _rhsconvn + fv_tmdp_cont
if loc_treat_nonl_explct and not closed_loop:
fvn_c = fv + rhsv_conbc_n + _rhsconvn + fv_tmdp_cont
if closed_loop:
if static_feedback:
mtxtb_n = dou.\
load_npa(feedbackthroughdict[None]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[None]['w'])
# fb = np.dot(tb_mat*mtxtb_n.T, v_old)
# print '\nnorm of feedback: ', np.linalg.norm(fb)
# print '\nnorm of v_old: ', np.linalg.norm(v_old)
else:
mtxtb_n = dou.load_npa(feedbackthroughdict[t]['mtxtb'])
w_n = dou.load_npa(feedbackthroughdict[t]['w'])
fvn_n = fvn_n + tb_mat * (tb_mat.T * w_n)
vmat_n = mtxtb_n.T
try:
umat_n = np.array(tb_mat.todense())
except AttributeError:
umat_n = tb_mat
else:
vmat_n = None
umat_n = None
(solvmat, rhsv, umat,
vmat) = _get_mats_rhs_ts(mmat=M, dt=cts, var_c=v_old,
coeffmat_c=A + convc_mat_c,
coeffmat_n=A + convc_mat_n,
fv_c=fvn_c, fv_n=fvn_n,
umat_c=umat_c, vmat_c=vmat_c,
umat_n=umat_n, vmat_n=vmat_n)
try:
if krpslvprms['krylovini'] == 'old':
krpslvprms['x0'] = vp_old
elif krpslvprms['krylovini'] == 'upd':
vp_oldold = vp_old
vp_old = vp_new
krpslvprms['x0'] = vp_old + \
cts*(vp_old - vp_oldold)/cts_old
cts_old = cts
except (TypeError, KeyError):
pass # no inival for krylov solver required
if loc_treat_nonl_explct and uniformgrid and not krylov:
if coeffmatlu is None:
print('gonna compute an LU of the coefficient ' +
'matrix \n and reuse it in the time stepping')
vp_new, coeffmatlu = \
lau.solve_sadpnt_smw(amat=solvmat, jmat=J, jmatT=JT,
rhsv=rhsv, rhsp=fp,
sadlu=coeffmatlu,
return_alu=True,
umat=umat, vmat=vmat)
else:
vp_new = lau.solve_sadpnt_smw(amat=solvmat,
jmat=J, jmatT=JT,
rhsv=rhsv,
rhsp=fp,
krylov=krylov,
krpslvprms=krpslvprms,
krplsprms=krplsprms,
umat=umat, vmat=vmat)
v_old = vp_new[:NV, ]
(umat_c, vmat_c, fvn_c,
convc_mat_c) = umat_n, vmat_n, fvn_n, convc_mat_n
dou.save_npa(_append_bcs_ornot(v_old),
fstring=cdatstr + '__vel')
_atdct(dictofvelstrs, t, cdatstr + '__vel')
p_new = -1/cts*vp_new[NV:, ]
# p was flipped and scaled for symmetry
if return_dictofpstrs:
dou.save_npa(p_new, fstring=cdatstr + '__p')
_atdct(dictofpstrs, t, cdatstr + '__p')
if return_as_list:
vellist.append(_append_bcs_ornot(v_old))
# integrate the Newton error
if stokes_flow or treat_nonl_explct:
norm_nwtnupd = None
elif comp_nonl_semexp_inig:
norm_nwtnupd = 1.
else:
if len(prev_v) > len(invinds):
prev_v = prev_v[invinds, :]
addtonwtnupd = cts * m_innerproduct(M, v_old - prev_v)
norm_nwtnupd += np.float(addtonwtnupd.flatten()[0])
if newtk == vel_nwtn_stps or norm_nwtnupd < loc_nwtn_tol:
# paraviewoutput in the (probably) last newton sweep
prvoutdict.update(dict(vc=v_old, pc=p_new, t=t))
dou.output_paraview(**prvoutdict)
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
print('\nnorm of current Newton update: {}'.format(norm_nwtnupd))
# print('\nsaved `norm_nwtnupd(={0})'.format(norm_nwtnupd) +
# ' to ' + cdatstr)
loc_treat_nonl_explct = False
comp_nonl_semexp_inig = False
cur_linvel_point = dictofvelstrs
iniv = v_old
if not treat_nonl_explct and lin_vel_point is None:
comp_nonl_semexp_inig = True
if addfullsweep and loctrng is loctrngs[-2]:
comp_nonl_semexp_inig = False
iniv = realiniv
loc_nwtn_tol = vel_nwtn_tol
elif loc_pcrd_stps:
vel_pcrd_stps = vel_loc_pcrd_steps
norm_nwtnupd = 1.
newtk = 0
if return_dictofvelstrs:
if return_dictofpstrs:
return dictofvelstrs, dictofpstrs
else:
return dictofvelstrs
elif return_as_list:
return vellist
else:
return
def solve_steadystate_nse(A=None, J=None, JT=None, M=None,
fv=None, fp=None,
V=None, Q=None, invinds=None, diribcs=None,
dbcvals=None, dbcinds=None,
diricontbcinds=None, diricontbcvals=None,
diricontfuncs=None,
return_vp=False, ppin=-1,
return_nwtnupd_norms=False,
N=None, nu=None,
vel_pcrd_stps=10, vel_pcrd_tol=1e-4,
vel_nwtn_stps=20, vel_nwtn_tol=5e-15,
clearprvdata=False,
useolddata=False,
vel_start_nwtn=None,
get_datastring=None,
data_prfx='',
paraviewoutput=False,
save_data=True,
save_intermediate_steps=False,
vfileprfx='', pfileprfx='',
verbose=True,
**kw):
"""
Solution of the steady state nonlinear NSE Problem
using Newton's scheme. If no starting value is provided, the iteration
is started with the steady state Stokes solution.
Parameters
----------
A : (N,N) sparse matrix
stiffness matrix aka discrete Laplacian, note the sign!
M : (N,N) sparse matrix
mass matrix
J : (M,N) sparse matrix
discrete divergence operator
JT : (N,M) sparse matrix, optional
discrete gradient operator, set to J.T if not provided
fv, fp : (N,1), (M,1) ndarrays
right hand sides restricted via removing the boundary nodes in the
momentum and the pressure freedom in the continuity equation
ppin : {int, None}, optional
which dof of `p` is used to pin the pressure, defaults to `-1`
dbcinds: list, optional
indices of the Dirichlet boundary conditions
dbcvals: list, optional
values of the Dirichlet boundary conditions (as listed in `dbcinds`)
diricontbcinds: list, optional
list of dirichlet indices that are to be controlled
diricontbcvals: list, optional
list of the vals corresponding to `diricontbcinds`
diricontfuncs: list, optional
list like `[ufunc]` where `ufunc: (t, v) -> u` where `u` is used to
scale the corresponding `diricontbcvals`
return_vp : boolean, optional
whether to return also the pressure, defaults to `False`
vel_pcrd_stps : int, optional
Number of Picard iterations when computing a starting value for the
Newton scheme, cf. Elman, Silvester, Wathen: *FEM and fast iterative
solvers*, 2005, defaults to `100`
vel_pcrd_tol : real, optional
tolerance for the size of the Picard update, defaults to `1e-4`
vel_nwtn_stps : int, optional
Number of Newton iterations, defaults to `20`
vel_nwtn_tol : real, optional
tolerance for the size of the Newton update, defaults to `5e-15`
Returns:
---
vel_k : (N, 1) ndarray
the velocity vector, if not `return_vp`, else
(v, p) : tuple
of the velocity and the pressure vector
norm_nwtnupd_list : list, on demand
list of the newton upd errors
"""
import sadptprj_riclyap_adi.lin_alg_utils as lau
if get_datastring is None:
get_datastring = get_datastr_snu
if JT is None:
JT = J.T
NV = J.shape[1]
#
# Compute or load the uncontrolled steady state Navier-Stokes solution
#
norm_nwtnupd_list = []
# a dict to be passed to the get_datastring function
datastrdict = dict(time=None, meshp=N, nu=nu,
Nts=None, data_prfx=data_prfx)
if clearprvdata:
cdatstr = get_datastring(**datastrdict)
for fname in glob.glob(cdatstr + '*__vel*'):
os.remove(fname)
if useolddata:
try:
cdatstr = get_datastring(**datastrdict)
norm_nwtnupd = dou.load_npa(cdatstr + '__norm_nwtnupd')
vel_k = dou.load_npa(cdatstr + '__vel')
norm_nwtnupd_list.append(norm_nwtnupd)
if verbose:
print('found vel files')
print('norm of last Nwtn update: {0}'.format(norm_nwtnupd))
print('... loaded from ' + cdatstr)
if np.atleast_1d(norm_nwtnupd)[0] is None:
norm_nwtnupd = None
pass # nothing useful found
elif norm_nwtnupd < vel_nwtn_tol:
if not return_vp:
return vel_k, norm_nwtnupd_list
else:
pfv = get_pfromv(v=vel_k[:NV, :], V=V,
M=M, A=A, J=J, fv=fv,
dbcinds=dbcinds, dbcvals=dbcvals,
invinds=invinds, diribcs=diribcs)
return (np.vstack([vel_k, pfv]), norm_nwtnupd_list)
except IOError:
if verbose:
print('no old velocity data found')
norm_nwtnupd = None
else:
# we start from scratch
norm_nwtnupd = None
if paraviewoutput:
cdatstr = get_datastring(**datastrdict)
vfile = dolfin.File(vfileprfx+'__steadystates.pvd')
pfile = dolfin.File(pfileprfx+'__steadystates.pvd')
prvoutdict = dict(V=V, Q=Q, vfile=vfile, pfile=pfile,
invinds=invinds, diribcs=diribcs, ppin=ppin,
dbcinds=dbcinds, dbcvals=dbcvals,
vp=None, t=None, writeoutput=True)
else:
prvoutdict = dict(writeoutput=False) # save 'if statements' later
NV = A.shape[0]
if vel_start_nwtn is None:
loccntbcinds, cntrlldbcvals, glbcntbcinds = [], [], []
if diricontbcinds is None or diricontbcinds == []:
cmmat, camat, cj, cjt, cfv, cfp = M, A, J, JT, fv, fp
cnv = NV
dbcntinvinds = invinds
else:
def _localizecdbinds(cdbinds):
""" find the local indices of the control dirichlet boundaries
the given control dirichlet boundaries were indexed w.r.t. the
full space `V`. Here, in the matrices, we have already
resolved the constant Dirichlet bcs
"""
allinds = np.arange(V.dim())
redcdallinds = allinds[invinds]
# now: find the positions of the control dbcs in the reduced
# index vector
lclinds = np.searchsorted(redcdallinds, cdbinds, side='left')
return lclinds
for k, cdbidbv in enumerate(diricontbcinds):
ccntrlfunc = diricontfuncs[k]
# no time at steady state, no starting value
cntrlval = ccntrlfunc(None, None)
localbcinds = (_localizecdbinds(cdbidbv)).tolist()
loccntbcinds.extend(localbcinds) # adding the boundary inds
glbcntbcinds.extend(cdbidbv)
ccntrlldbcvals = [cntrlval*bcvl for bcvl in diricontbcvals[k]]
# adding the scaled boundary values
cntrlldbcvals.extend(ccntrlldbcvals)
dbcntinvinds = np.setdiff1d(invinds, glbcntbcinds).astype(np.int32)
matdict = dict(M=M, A=A, J=J, JT=JT, MP=None)
cmmat, camat, cjt, cj, _, cfv, cfp, _ = dts.\
condense_sysmatsbybcs(matdict, dbcinds=loccntbcinds,
dbcvals=cntrlldbcvals, mergerhs=True,
rhsdict=dict(fv=fv, fp=fp),
ret_unrolled=True)
cnv = cmmat.shape[0]
vp_stokes = lau.solve_sadpnt_smw(amat=camat, jmat=cj, jmatT=cjt,
rhsv=cfv, rhsp=cfp)
vp_stokes[cnv:] = -vp_stokes[cnv:]
# pressure was flipped for symmetry
# save the data
cdatstr = get_datastring(**datastrdict)
if save_data:
dou.save_npa(vp_stokes[:cnv, ], fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_stokes,
dbcinds=[dbcinds, glbcntbcinds],
dbcvals=[dbcvals, cntrlldbcvals],
invinds=dbcntinvinds))
dou.output_paraview(**prvoutdict)
# Stokes solution as starting value
vp_k = vp_stokes
vel_k = vp_stokes[:cnv, ]
else:
vel_k = vel_start_nwtn
matdict = dict(M=M, A=A, J=J, JT=JT, MP=None)
rhsdict = dict(fv=fv, fp=fp)
cndnsmtsdct = dict(dbcinds=loccntbcinds, mergerhs=True,
ret_unrolled=True)
# Picard iterations for a good starting value for Newton
for k in range(vel_pcrd_stps):
cntrlldbcvals = _unroll_cntrl_dbcs(diricontbcvals, diricontfuncs,
time=None, vel=vel_k)
(convc_mat,
rhs_con, rhsv_conbc) = \
get_v_conv_conts(prev_v=vel_k, V=V, diribcs=diribcs,
invinds=dbcntinvinds,
dbcinds=[dbcinds, glbcntbcinds],
dbcvals=[dbcvals, cntrlldbcvals], Picard=True)
_, _, _, _, _, cfv, cfp, _ = dts.\
condense_sysmatsbybcs(matdict, dbcvals=cntrlldbcvals,
rhsdict=rhsdict, **cndnsmtsdct)
vp_k = lau.solve_sadpnt_smw(amat=camat+convc_mat, jmat=cj, jmatT=cjt,
rhsv=cfv+rhsv_conbc, rhsp=cfp)
# vp_k = lau.solve_sadpnt_smw(amat=A+convc_mat, jmat=J, jmatT=JT,
# rhsv=fv+rhsv_conbc,
# rhsp=fp)
normpicupd = np.sqrt(m_innerproduct(cmmat, vel_k-vp_k[:cnv, ]))[0]
if verbose:
print('Picard iteration: {0} -- norm of update: {1}'.
format(k+1, normpicupd))
vel_k = vp_k[:cnv, ]
vp_k[cnv:] = -vp_k[cnv:]
# pressure was flipped for symmetry
if normpicupd < vel_pcrd_tol:
break
# Newton iteration
for vel_newtk, k in enumerate(range(vel_nwtn_stps)):
cdatstr = get_datastring(**datastrdict)
cntrlldbcvals = _unroll_cntrl_dbcs(diricontbcvals, diricontfuncs,
time=None, vel=vel_k)
_, _, _, _, _, cfv, cfp, _ = dts.\
condense_sysmatsbybcs(matdict, dbcvals=cntrlldbcvals,
rhsdict=rhsdict, **cndnsmtsdct)
(convc_mat, rhs_con, rhsv_conbc) = \
get_v_conv_conts(prev_v=vel_k, V=V, diribcs=diribcs,
invinds=dbcntinvinds,
dbcinds=[dbcinds, glbcntbcinds],
dbcvals=[dbcvals, cntrlldbcvals])
vp_k = lau.solve_sadpnt_smw(amat=camat+convc_mat, jmat=cj, jmatT=cjt,
rhsv=cfv+rhs_con+rhsv_conbc,
rhsp=cfp)
norm_nwtnupd = np.sqrt(m_innerproduct(cmmat, vel_k - vp_k[:cnv, :]))[0]
vel_k = vp_k[:cnv, ]
vp_k[cnv:] = -vp_k[cnv:]
# pressure was flipped for symmetry
if verbose:
print('Steady State NSE: Newton iteration: {0}'.format(vel_newtk) +
'-- norm of update: {0}'.format(norm_nwtnupd))
if save_data:
dou.save_npa(vel_k, fstring=cdatstr + '__vel')
prvoutdict.update(dict(vp=vp_k, dbcvals=[dbcvals, cntrlldbcvals]))
dou.output_paraview(**prvoutdict)
if norm_nwtnupd < vel_nwtn_tol:
break
else:
if vel_nwtn_stps == 0:
print('No Newton steps = steady state probably not well converged')
else:
raise UserWarning('Steady State NSE: Newton has not converged')
if save_data:
dou.save_npa(norm_nwtnupd, cdatstr + '__norm_nwtnupd')
prvoutdict.update(dict(vp=vp_k, dbcvals=[dbcvals, cntrlldbcvals]))
dou.output_paraview(**prvoutdict)
# savetomatlab = True
# if savetomatlab:
# export_mats_to_matlab(E=None, A=None, matfname='matexport')
vwc = _attach_cntbcvals(vel_k.flatten(), globbcinvinds=dbcntinvinds,
globbcinds=glbcntbcinds, dbcvals=cntrlldbcvals,
invinds=invinds, NV=V.dim())
if return_vp:
retthing = (vwc.reshape((NV, 1)), vp_k[cnv:, :])
else:
retthing = vwc.reshape((NV, 1))
if return_nwtnupd_norms:
return retthing, norm_nwtnupd_list
else:
return retthing
def test_qbdae_ass(problemname='cylinderwake',
N=1,
Re=None,
nu=3e-2,
t0=0.0,
tE=1.0,
Nts=100,
use_saved_mats=None):
trange = np.linspace(t0, tE, Nts + 1)
DT = (tE - t0) / Nts
rdir = 'results/'
ddir = 'data/'
if use_saved_mats is None:
femp, stokesmatsc, rhsd_vfrc, rhsd_stbc = \
dns.problem_setups.get_sysmats(problem=problemname, N=N, Re=Re)
invinds = femp['invinds']
A, J, M = stokesmatsc['A'], stokesmatsc['J'], stokesmatsc['M']
L = 0 * A
fvc, fpc = rhsd_vfrc['fvc'], rhsd_vfrc['fpr']
fv_stbc, fp_stbc = rhsd_stbc['fv'], rhsd_stbc['fp']
hstr = ddir + problemname + '_N{0}_hmat'.format(N)
try:
hmat = dou.load_spa(hstr)
print('loaded `hmat`')
except IOError:
print('assembling hmat ...')
hmat = dnsts.ass_convmat_asmatquad(W=femp['V'], invindsw=invinds)
dou.save_spa(hmat, hstr)
invinds = femp['invinds']
NV, NP = invinds.shape[0], J.shape[0]
zerv = np.zeros((NV, 1))
bc_conv, bc_rhs_conv, rhsbc_convbc = \
snu.get_v_conv_conts(prev_v=zerv, V=femp['V'], invinds=invinds,
diribcs=femp['diribcs'], Picard=False)
fp = fp_stbc + fpc
fv = fv_stbc + fvc - bc_rhs_conv
if linnsesol:
vp_nse, _ = snu.\
solve_steadystate_nse(A=A, J=J, JT=None, M=M,
fv=fv_stbc + fvc,
fp=fp_stbc + fpc,
V=femp['V'], Q=femp['Q'],
invinds=invinds,
diribcs=femp['diribcs'],
return_vp=False, ppin=-1,
N=N, nu=nu,
clearprvdata=False)
old_v = vp_nse[:NV]
else:
import sadptprj_riclyap_adi.lin_alg_utils as lau
# Stokes solution as initial value
vp_stokes = lau.solve_sadpnt_smw(amat=A,
jmat=J,
rhsv=fv_stbc + fvc,
rhsp=fp_stbc + fpc)
old_v = vp_stokes[:NV]
sysmat = sps.vstack([
sps.hstack([M + DT * (A + bc_conv), J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])
])
if use_saved_mats is not None:
# if saved as in ../get_exp_mats
import scipy.io
mats = scipy.io.loadmat(use_saved_mats)
A = -mats['A']
L = -mats['L']
Re = mats['Re']
N = A.shape[0]
M = mats['M']
J = mats['J']
hmat = -mats['H']
fv = mats['fv']
fp = mats['fp']
NV, NP = fv.shape[0], fp.shape[0]
old_v = mats['ss_stokes']
sysmat = sps.vstack([
sps.hstack([M + DT * A, J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])
])
if compevs:
import matplotlib.pyplot as plt
import scipy.linalg as spla
hlstr = ddir + problemname + '_N{0}_Re{1}Nse{2}_hlmat'.\
format(N, Re, linnsesol)
HL = linearzd_quadterm(hmat, old_v, hlstr=hlstr)
print(HL.shape)
asysmat = sps.vstack([
sps.hstack([-(A - L + HL), J.T]),
sps.hstack([J, sps.csc_matrix((NP, NP))])
])
msysmat = sps.vstack([
sps.hstack([M, sps.csc_matrix((NV, NP))]),
sps.hstack([sps.csc_matrix((NP, NV)),
sps.csc_matrix((NP, NP))])
])
levstr = ddir + problemname + '_N{0}Re{1}Nse{2}_levs'.\
format(N, Re, linnsesol)
try:
levs = dou.load_npa(levstr)
if debug:
raise IOError()
print('loaded the eigenvalues of the linearized system')
except IOError:
print('computing the eigenvalues of the linearized system')
A = asysmat.todense()
M = msysmat.todense()
levs = spla.eigvals(A, M, overwrite_a=True, check_finite=False)
dou.save_npa(levs, levstr)
plt.figure(1)
# plt.xlim((-25, 15))
# plt.ylim((-50, 50))
plt.plot(np.real(levs), np.imag(levs), '+')
plt.show(block=False)
if timeint:
print('computing LU once...')
sysmati = spsla.factorized(sysmat)
vfile = dolfin.File(rdir + problemname + 'qdae__vel.pvd')
pfile = dolfin.File(rdir + problemname + 'qdae__p.pvd')
prvoutdict = dict(V=femp['V'],
Q=femp['Q'],
vfile=vfile,
pfile=pfile,
invinds=invinds,
diribcs=femp['diribcs'],
vp=None,
t=None,
writeoutput=True)
print('doing the time loop...')
for t in trange:
crhsv = M * old_v + DT * (fv - hmat * np.kron(old_v, old_v))
crhs = np.vstack([crhsv, fp])
vp_new = np.atleast_2d(sysmati(crhs.flatten())).T
prvoutdict.update(dict(vp=vp_new, t=t))
dou.output_paraview(**prvoutdict)
old_v = vp_new[:NV]
print(t, np.linalg.norm(old_v))
