/
rothe_main.py
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/
rothe_main.py
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import dolfin
import numpy as np
import dolfin_navier_scipy.stokes_navier_utils as snu
import dolfin_navier_scipy.data_output_utils as dou
import dolfin_navier_scipy.dolfin_to_sparrays as dts
import matlibplots.conv_plot_utils as cpu
import rothe_utils as rtu
from time_int_schemes import get_dtstr
dolfin.parameters.linear_algebra_backend = 'uBLAS'
import logging
# logging.basicConfig(level=logging.DEBUG)
logging.basicConfig(level=logging.INFO)
logger = logging.getLogger("rothemain")
# disable the fenics loggers
logging.getLogger('UFL').setLevel(logging.WARNING)
logging.getLogger('FFC').setLevel(logging.WARNING)
logger.setLevel('INFO') # default is DEBUG
fh = logging.FileHandler('log.rothemain')
# fh.setLevel(logging.DEBUG)
fh.setLevel(logging.INFO)
formatter = \
logging.Formatter('%(asctime)s - %(name)s - %(levelname)s - %(message)s')
# logging.Formatter('%(name)s - %(levelname)s - %(message)s')
fh.setFormatter(formatter)
logger.addHandler(fh)
'''
Idea of code
- define reference FEM spaces `Vref`, `Qref` (fine)
- compute initial value `vini` on the refspacs and use it as first `vprev`
- compute `vref`, `pref` on the refspacs using `solve_nse`
- define `Vplt`, `Qplt` for plotting (rough)
- time loop:
- define/get the current spaces `Vcur`, `Qcur`
- comp `vcur`, `pcur` based on `vprev`
- comp `and collect norm(vcur - vref)` and `norm(pcur - pref)`
- plot `vcur`, `pcur` interpolated in the refspacs
Issues:
- save the `v` variables with boundary conditions, because
- otherwise `diribcs` have to be saved with the data as well
- easier for visualization and error estimation
- save `v` and `p` separately
- to append the bcs, `v` is separated anyways
- that is coherent with `solve_nse`
'''
proutdir = 'results/'
ddir = 'data/'
debug = True
debug = False
def check_the_sim(problem='cylinderwake', nswtchsl=[2], scheme='CR',
nu=None, Re=None, Nts=None, paraout=False, t0=None, tE=None,
plotit=False, dtstrdct={}, debug=False, Nref=3,
method=2, refmethod=2):
trange = np.linspace(t0, tE, Nts+1)
refdtstrdct = dict(prefix=ddir+problem+scheme,
method=refmethod, N=None, Nts=Nts, t0=t0, te=tE)
refdatstr = get_dtstr(t=None, **refdtstrdct)
compargs = dict(problem=problem, N=Nref, nu=nu, Re=Re, trange=trange,
scheme=scheme, data_prefix=refdatstr, debug=debug)
refvdict, refpdict = dou.load_or_comp(filestr=[refdatstr+'_refvdict',
refdatstr+'_refpdict'],
comprtn=gettheref,
comprtnargs=compargs,
debug=False, itsadict=True)
viniv = dou.load_npa(refvdict['{0}'.format(t0)])
piniv = dou.load_npa(refpdict['{0}'.format(t0)])
# set up the list of the mesh parameters at every time step
swl = Nts/len(nswtchsl)
Nll = np.array([nswtchsl[0]]*(Nts+1))
for k, N in enumerate(nswtchsl[1:]):
Nll[(k+1)*swl+1:] = N
Nll[0] = Nref
Nll = Nll.tolist()
nswtchstr = 'Nswitches' + ''.join(str(e) for e in nswtchsl)
dtstrdct['prefix'] = dtstrdct['prefix'] + nswtchstr
dtstrdct.update(t=None)
cdatstr = get_dtstr(**dtstrdct)
compvpdargs = dict(problem=problem, scheme=scheme, Re=Re, nu=nu,
t0=t0, tE=tE, Nts=Nts, viniv=viniv, piniv=piniv,
Nini=Nref, Nll=Nll, dtstrdct=dtstrdct, method=method)
logger.info('try to load `' + cdatstr + '_vdict`, `' + cdatstr + '_pdict`')
vdict, pdict = dou.load_or_comp(filestr=[cdatstr+'_vdict',
cdatstr+'_pdict'],
comprtn=rtu.rothe_time_int,
comprtnargs=compvpdargs,
debug=debug, itsadict=True)
# vdict, pdict = rtu.rothe_ind2(problem=problem, scheme=scheme,
# Re=Re, nu=nu,
# t0=t0, tE=tE, Nts=Nts,
# viniv=viniv, piniv=piniv, Nini=Nref,
# Nll=Nll, dtstrdct=dtstrdct)
compvperrargs = dict(problem=problem, scheme=scheme,
trange=trange.tolist(),
rvd=refvdict, rpd=refpdict, Nref=Nref,
cvd=vdict, cpd=pdict, Nll=Nll)
errdict = dou.load_or_comp(filestr=[cdatstr+'_vperrdict'],
comprtn=compvperr, debug=debug,
comprtnargs=compvperrargs, itsadict=True)
if plotit:
rtu.plottimeerrs(trange=trange, perrl=[errdict['perrl']],
verrl=[errdict['verrl']], showplot=True)
return (errdict['verrl'], errdict['perrl'],
errdict['verrint'], errdict['perrint'], trange.tolist())
def compvperr(problem=None, scheme=None, trange=None,
rvd=None, rpd=None, Nref=None,
cvd=None, cpd=None, Nll=None):
verrl, perrl = [], []
rmd = rtu.get_curmeshdict(problem=problem, N=Nref,
scheme=scheme, onlymesh=True)
for tk, t in enumerate(trange):
vref = dou.load_npa(rvd['{0}'.format(t)])
pref = dou.load_npa(rpd['{0}'.format(t)])
# vreff, preff = dts.\
# expand_vp_dolfunc(vc=vref, V=rmd['V'], pc=pref, Q=rmd['Q'])
cmd = rtu.get_curmeshdict(problem=problem, N=Nll[tk],
scheme=scheme, onlymesh=True)
try:
vcur = dou.load_npa(cvd[t])
pcur = dou.load_npa(cpd[t])
except KeyError:
vcur = dou.load_npa(cvd['{0}'.format(t)])
pcur = dou.load_npa(cpd['{0}'.format(t)])
logger = logging.getLogger("rothemain.compvperr")
logger.debug("len v={0}, dim V={1}".format(vcur.size, cmd['V'].dim()))
vcurf, pcurf = dts.\
expand_vp_dolfunc(vc=vcur, V=cmd['V'], pc=pcur, Q=cmd['Q'])
# # # This would be the FEniCS way to compute the diff
#
# verrl.append(dolfin.errornorm(vreff, vcurf, degree_rise=2))
#
# # # however this gave strange results (due to rounding errs?)
# # # instead we interpolate and substract manually
Vref = rmd['V']
vcfinvref = dolfin.interpolate(vcurf, Vref)
vcinvrefvec = vcfinvref.vector().array()
difffunc = dolfin.Function(Vref)
difffunc.vector().set_local(vref.flatten()-vcinvrefvec)
Qref = rmd['Q']
pcfinvref = dolfin.interpolate(pcurf, Qref)
pcinvrefvec = pcfinvref.vector().array()
difffuncp = dolfin.Function(Qref)
difffuncp.vector().set_local(pref.flatten()-pcinvrefvec)
verrl.append(dolfin.norm(difffunc))
perrl.append(dolfin.norm(difffuncp))
pverr, pperr, pt = verrl[0], perrl[0], trange[0]
verrint, perrint = 0, 0
for k in range(len(trange)-1):
cverr, cperr, ct = verrl[k+1], perrl[k+1], trange[k+1]
cts = ct - pt
logger.debug('t={0}, cts={3}, cverr={1}, verrint={2}'.
format(ct, cverr, verrint, cts))
verrint += 0.5*cts*(pverr + cverr)
perrint += 0.5*cts*(pperr + cperr)
pverr, pperr, pt = cverr, cperr, ct
return dict(verrl=verrl, perrl=perrl, trange=trange,
perrint=perrint, verrint=verrint,
Nll=Nll, Nref=Nref)
def gettheref(problem='cylinderwake', N=None, nu=None, Re=None, Nts=None,
paraout=False, trange=None, scheme=None, data_prefix='',
debug=False):
refmeshdict = rtu.get_curmeshdict(problem=problem, N=N, nu=nu,
Re=Re, scheme=scheme)
refvdict, refpdict = snu.\
solve_nse(trange=trange, clearprvdata=debug, data_prfx=data_prefix,
vfileprfx=proutdir, pfileprfx=proutdir,
output_includes_bcs=True,
return_dictofvelstrs=True, return_dictofpstrs=True,
dictkeysstr=True,
start_ssstokes=True, **refmeshdict)
return refvdict, refpdict
if __name__ == '__main__':
problem = 'cylinderwake'
scheme = 'CR'
Re = 60
Nref = 3
Ntslist = [2048, 4096] # [16]
methlist = [1, 2] # {1: 'smaminex', 2: 'ind2'}
t0, tE = 0.0, 2.0
nswtchshortlist = [3, 2, 3] # , 2, 3] # we recommend to start with `Nref`
verrl, perrl, tmeshl = [], [], []
legl = []
keeppointslist = []
for method in methlist:
for Nts in Ntslist:
dtstrdct = dict(prefix=ddir+problem+scheme, Nref=Nref,
method=method, N=None, Nts=Nts, t0=t0, te=tE)
verr, perr, perrint, verrint, tmesh = \
check_the_sim(problem='cylinderwake', method=method,
nswtchsl=nswtchshortlist, scheme='CR', Re=Re,
Nts=Nts, paraout=False, t0=t0, tE=tE,
dtstrdct=dtstrdct, debug=debug)
tmeshl.append(tmesh[1:])
verrl.append(verr[1:])
perrl.append(perr[1:])
nswtchstr = 'N' + ''.join(str(e) for e in nswtchshortlist)
legl.append('$\\mathsf{{Nts}}={0}$ (index-{1})'.
format(Nts, method))
logger.info(nswtchstr + ': Nts={0}, m={1}, veint={2}, peint={3}'.
format(Nts, method, verrint, perrint))
curptkl = []
for k in np.arange(1, len(nswtchshortlist)):
jumpindx = k*(len(tmesh)-1)/len(nswtchshortlist) # an int !!
curptkl.extend([jumpindx-1, jumpindx])
keeppointslist.append(curptkl)
# markerl = ['s', '^', '.', '*', 'o', '+']
xticks = np.linspace(t0, tE, 5)
ppltdict = dict(leglist=legl, xlabel='t', xticks=xticks, logscaley=2,
usedefaultmarkers=True)
cpu.para_plot(None, perrl, abscissal=tmeshl, fignum=11,
title='pointwise error in $p$',
tikzfile='p-pointwiseerror.tex',
xlims=[t0, tE],
downsample=50, keeppointslist=keeppointslist,
**ppltdict)
cpu.para_plot(None, verrl, abscissal=tmeshl, fignum=22,
title='pointwise error in $q$',
tikzfile='vel-pointwiseerror.tex',
xlims=[t0, tE],
downsample=50,
**ppltdict)