def get_conv_curfv_rearr(v,PrP,tcur,B2BoolInv):
ConV = dtn.get_convvec(v, PrP.V)
ConV = ConV[PrP.invinds,]
ConV = np.vstack([ConV[~B2BoolInv],ConV[B2BoolInv]])
CurFv = dtn.get_curfv(PrP.V, PrP.fv, PrP.invinds, tcur)
if len(CurFv) != len(PrP.invinds):
raise Warning('Need fv at innernodes here')
CurFv = np.vstack([CurFv[~B2BoolInv],CurFv[B2BoolInv]])
return ConV, CurFv
def test_linearized_mat_NSE_form(self):
"""check the conversion: dolfin form <-> numpy arrays
and the linearizations"""
import dolfin_to_nparrays as dtn
u = self.fenics_sol_u
u.t = 1.0
ufun = dolfin.project(u, self.V)
uvec = ufun.vector().array().reshape(len(ufun.vector()), 1)
N1, N2, fv = dtn.get_convmats(u0_dolfun=ufun, V=self.V)
conv = dtn.get_convvec(u0_dolfun=ufun, V=self.V)
self.assertTrue(np.allclose(conv, N1 * uvec))
self.assertTrue(np.allclose(conv, N2 * uvec))
def test_eul_solution(self):
from dolfin import project
import prob_defs as tts
import dolfin_to_nparrays as dtn
from numpy import log
nu = 0
def get_funcexpr_as_vec(u, U, invinds=None, t=None):
if t is not None:
u.t = t
if invinds is None:
invinds = range(U.dim())
ua = project(u, U)
ua = ua.vector()
ua = ua.array()
return ua
eoca = np.zeros(len(self.Nlist))
eocc = np.zeros(len(self.Nlist))
for k, N in enumerate(self.Nlist):
PrP = tts.ProbParams(N, omega=8, nu=nu)
# get system matrices as np.arrays
Ma, Aa, BTa, Ba, MPa = dtn.get_sysNSmats(PrP.V, PrP.Q)
tcur = self.tcur
PrP.fv.t = tcur
PrP.fv.nu = nu # nu = 0, for Eulerian Flow - no diffusion
fv, fp = dtn.setget_rhs(PrP.V, PrP.Q, PrP.fv, PrP.fp)
Mc, Ac, BTc, Bc, fvbc, fpbc, bcinds, bcvals, invinds = \
dtn.condense_sysmatsbybcs(Ma, Aa, BTa, Ba, fv, fp, PrP.velbcs)
v, vdot, p = PrP.v, PrP.vdot, PrP.p
vc = get_funcexpr_as_vec(v, PrP.V, t=tcur)
pc = get_funcexpr_as_vec(p, PrP.Q, t=tcur)
vdotc = get_funcexpr_as_vec(vdot, PrP.V, t=tcur)
v.t = tcur
vf = project(v, PrP.V)
ConV = dtn.get_convvec(vf, PrP.V)
resV = Ma*vdotc + nu*Aa*vc + ConV[:, 0] - BTa*pc - fv[:, 0]
resVc = Mc*vdotc[invinds] + nu*Ac*vc[invinds] + ConV[invinds, 0] -\
BTc*pc - fvbc[:, 0] - fv[invinds, 0]
eoca[k] = np.sqrt(np.dot(np.atleast_2d(resV[invinds]),
Mc*np.atleast_2d(resV[invinds]).T))
eocc[k] = np.sqrt(np.dot(np.atleast_2d(resVc),
Mc*np.atleast_2d(resVc).T))
eocs = np.array([log(eoca[0] / eoca[1]),
log(eoca[1] / eoca[2]),
log(eocc[0] / eocc[1]),
log(eocc[1] / eocc[2])])
OC = self.OC
print eocs
print np.array([OC*log(2)]*4)
self.assertTrue((eocs > [np.array([OC*log(2)])]*4).all())
def halfexp_euler_nseind2(Mc,MP,Ac,BTc,Bc,fvbc,fpbc,vp_init,PrP,TsP): """halfexplicit euler for the NSE in index 2 formulation """ #### # # Basic Eqn: # # 1/dt*M -B.T q+ 1/dt*M*qc - K(qc) + fc # B * pc = g # ######## Nts, t0, tE, dt, Nv, Np = init_time_stepping(PrP,TsP) tcur = t0 MFac = 1 CFac = 1 #/dt PFac = -1 #-1 for symmetry (if CFac==1) PFacI = -1 v, p = expand_vp_dolfunc(PrP, vp=vp_init, vc=None, pc=None) TsP.UpFiles.u_file << v, tcur TsP.UpFiles.p_file << p, tcur IterAv = MFac*sps.hstack([1.0/dt*Mc,PFacI*(-1)*BTc[:,:-1]]) IterAp = CFac*sps.hstack([Bc[:-1,:],sps.csr_matrix((Np-1,Np-1))]) IterA = sps.vstack([IterAv,IterAp]) MPc = MP[:-1,:][:,:-1] vp_old = vp_init ContiRes, VelEr, PEr, TolCorL = [], [], [], [] # M matrix for the minres routine # M accounts for the FEM discretization def _MInv(vp): v, p = vp[:Nv,], vp[Nv:,] Mv = krypy.linsys.cg(Mc,v,tol=1e-14)['xk'] Mp = krypy.linsys.cg(MPc,p,tol=1e-14)['xk'] return np.vstack([Mv,Mp]) MInv = spsla.LinearOperator( (Nv+Np-1,Nv+Np-1), matvec=_MInv, dtype=np.float32 ) def ind2_ip(vp1,vp2): """ for applying the fem inner product """ v1, v2 = vp1[:Nv,], vp2[:Nv,] p1, p2 = vp1[Nv:,], vp2[Nv:,] return mass_fem_ip(v1,v2,Mc) + mass_fem_ip(p1,p2,MPc) for etap in range(1,TsP.NOutPutPts + 1 ): for i in range(Nts/TsP.NOutPutPts): ConV = dtn.get_convvec(v, PrP.V) CurFv = dtn.get_curfv(PrP.V, PrP.fv, PrP.invinds, tcur) Iterrhs = np.vstack([MFac*1.0/dt*Mc*vp_old[:Nv,],np.zeros((Np-1,1))]) \ + np.vstack([MFac*(fvbc+CurFv-ConV[PrP.invinds,]), CFac*fpbc[:-1,]]) if TsP.linatol == 0: vp_new = spsla.spsolve(IterA,Iterrhs)#,vp_old,tol=TsP.linatol) vp_old = np.atleast_2d(vp_new).T else: if TsP.TolCorB: NormRhsInd2 = np.sqrt(ind2_ip(Iterrhs,Iterrhs))[0][0] TolCor = 1.0 / np.max([NormRhsInd2,1]) else: TolCor = 1.0 ret = krypy.linsys.minres(IterA, Iterrhs, x0=vp_old, tol=TolCor*TsP.linatol, M=MInv) vp_old = ret['xk'] print 'Needed %d iterations -- final relres = %e' %(len(ret['relresvec']), ret['relresvec'][-1] ) print 'TolCor was %e' % TolCor vc = vp_old[:Nv,] pc = PFacI*vp_old[Nv:,] v, p = expand_vp_dolfunc(PrP, vp=None, vc=vc, pc=pc) tcur += dt # the errors vCur, pCur = PrP.v, PrP.p vCur.t = tcur pCur.t = tcur - dt ContiRes.append(comp_cont_error(v,fpbc,PrP.Q)) VelEr.append(errornorm(vCur,v)) PEr.append(errornorm(pCur,p)) TolCorL.append(TolCor) print '%d of %d time steps completed ' % (etap*Nts/TsP.NOutPutPts, Nts) if TsP.ParaviewOutput: TsP.UpFiles.u_file << v, tcur TsP.UpFiles.p_file << p, tcur TsP.Residuals.ContiRes.append(ContiRes) TsP.Residuals.VelEr.append(VelEr) TsP.Residuals.PEr.append(PEr) TsP.TolCor.append(TolCorL) return
Mc, Ac, BTc, Bc, fvbc, fpbc, bcinds, bcvals, invinds = \ dtn.condense_sysmatsbybcs(Ma,Aa,BTa,Ba,fv,fp,PrP.velbcs) v, vdot, p = PrP.v, PrP.vdot, PrP.p def get_funcexpr_as_vec(u, U, invinds=None, t=None): if t is not None: u.t = t if invinds is None: invinds = range(U.dim()) ua = project(u,U) ua = ua.vector() ua = ua.array() #uc = np.atleast_2d(ua[invinds].T) return ua vc = get_funcexpr_as_vec(v, PrP.V, t=tcur) pc = get_funcexpr_as_vec(p, PrP.Q, t=tcur) vdotc = get_funcexpr_as_vec(vdot, PrP.V, t=tcur) v.t = tcur vf = project(v, PrP.V) ConV = dtn.get_convvec(vf, PrP.V) resV = Ma*vdotc + nu*Aa*vc + ConV[:,0] - BTa*pc - fv[:,0] resVc = Mc*vdotc[invinds] + nu*Ac*vc[invinds] + ConV[invinds,0] - BTc*pc - fvbc[:,0] - fv[invinds,0] print np.dot(np.atleast_2d(resV[invinds]),Mc*np.atleast_2d(resV[invinds]).T) print np.dot(np.atleast_2d(resVc),Mc*np.atleast_2d(resVc).T)