def app_pverr(tcur):
cdatstr = get_dtstr(t=tcur, **dtstrdct)
vp = np.load(cdatstr + '.npy')
v, p = expand_vp_dolfunc(PrP, vp=vp)
# vpref = np.load(cdatstrref + '.npy')
# vref, pref = expand_vp_dolfunc(PrP, vp=vpref)
vref = np.load(vdref[tcur] + '.npy')
pref = np.load(pdref[tcur] + '.npy')
# vpref = np.vstack([vref, pref])
vreff, preff = expand_vp_dolfunc(PrP, vc=vref, pc=pref)
# vdiff, pdiff = expand_vp_dolfunc(PrP, vc=vp[:Nv]-vref,
# pc=vp[Nv:]-pref)
# prtrial = snu.get_pfromv(v=vref, **snsedict)
# vrtrial, prtrial = expand_vp_dolfunc(PrP, vc=vref, pc=prtrial)
# print 'pref', dolfin.norm(preff)
# print 'p', dolfin.norm(p)
# print 'p(v)', dolfin.norm(ptrial)
# print 'p(vref){0}\n'.format(dolfin.norm(prtrial))
elv.append(dolfin.errornorm(v, vreff))
elp.append(dolfin.errornorm(p, preff))
# elv.append(dolfin.norm(vdiff))
# elp.append(dolfin.norm(pdiff))
cres = J*vp[:Nv]-fpbc
mpires = (Mpfac.solve(cres.flatten())).reshape((cres.size, 1))
ncres = np.sqrt(np.dot(cres.T, mpires))[0][0]
# ncres = np.sqrt(np.dot(cres.T, MP*cres))[0][0]
# routine from time_int_schemes seems buggy for CR or 'g not 0'
# ncres = comp_cont_error(v, fpbc, PrP.Q)
elc.append(ncres)
def abetterworld(N = 20, Nts = [16, 32, 64, 128]):
tip = time_int_params()
prp = problem_params(N)
fv, fp, sol_v, sol_p = prp['fv'], prp['fp'], prp['sol_v'], prp['sol_p']
# fixing some parameters
# fv.om, v_sol.om, p_sol.om = 1, 1, 1
# fv.nu, v_sol.nu, p_sol.nu = 1, 1, 1
###
## start with the Stokes problem for initialization
###
stokesmats = dtn.get_stokessysmats(prp['V'], prp['Q'],
tip['nu'])
rhsd_vf = dtn.setget_rhs(prp['V'], prp['Q'],
prp['fv'], prp['fp'], t=0)
# remove the freedom in the pressure
stokesmats['J'] = stokesmats['J'][:-1,:][:,:]
stokesmats['JT'] = stokesmats['JT'][:,:-1][:,:]
rhsd_vf['fp'] = rhsd_vf['fp'][:-1,:]
# reduce the matrices by resolving the BCs
(stokesmatsc,
rhsd_stbc,
INVINDS,
bcinds,
bcvals) = dtn.condense_sysmatsbybcs(stokesmats,
prp['bc0'])
# casting some parameters
NV, NP = len(INVINDS), stokesmats['J'].shape[0]
M, A, J = stokesmatsc['M'], stokesmatsc['A'], stokesmatsc['J']
###
## Compute the time-dependent flow
###
inivalvec = np.zeros((NV+NP,1))
for nts in Nts:
DT = (1.0*tip['t0'] - tip['tE'])/nts
biga = sps.vstack([
sps.hstack([M+DT*A, J.T]),
sps.hstack([J, sps.csr_matrix((NP, NP))])
])
vp_old = inivalvec
ContiRes, VelEr, PEr = [], [], []
for tcur in np.linspace(tip['t0']+DT,tip['tE'],nts):
fvpn = dtn.setget_rhs(prp['V'], prp['Q'], fv, fp, t=tcur)
cur_rhs = np.vstack([fvpn['fv'][INVINDS,:],
np.zeros((NP,1))])
vp_old = krypy.linsys.minres(biga, cur_rhs,
x0=vp_old, maxiter=100)['xk']
vc = vp_old[:NV,]
pc = vp_old[NV:,]
v, p = tis.expand_vp_dolfunc(tip, vp=None, vc=vc, pc=pc)
v_sol.t, p_sol.t = tcur
# the errors
ContiRes.append(tis.comp_cont_error(v,fp,tip['Q']))
VelEr.append(errornorm(vCur,v))
PEr.append(errornorm(pCur,p))
tip['Residuals'].ContiRes.append(ContiRes)
tip['Residuals'].VelEr.append(VelEr)
tip['Residuals'].PEr.append(PEr)
