def NSMatrixSetup(P, FS, A, nu, iter, Type):
if Type['precond'] == 'PCD':
u = TrialFunction(FS['Velocity'])
v = TestFunction(FS['Velocity'])
p = TrialFunction(FS['Pressure'])
q = TestFunction(FS['Pressure'])
IS = common.IndexSet([FS['Velocity']])
mesh = FS['Velocity'].mesh()
n = FacetNormal(mesh)
if iter == 1:
if FS['Pressure'].ufl_element().degree(
) == 0 or FS['Pressure'].ufl_element().family() == 'DG':
PrintFuncs.Errors(
'Navier-Stokes PCD preconditioner not implemented for DG pressure elements'
)
P['L'] = PETScFunc.Assemble(
assemble(nu * inner(grad(p), grad(q)) * dx))
P['M'] = PETScFunc.Assemble(assemble((1. / nu) * inner(p, q) * dx))
P['Fp'] = PETScFunc.Assemble(
assemble(nu * inner(grad(q), grad(p)) * dx(mesh) +
inner((Type['u_k'][0] * grad(p)[0] +
Type['u_k'][1] * grad(p)[1]), q) * dx(mesh) +
(1. / 2) * div(Type['u_k']) * inner(p, q) * dx(mesh) -
(1. / 2) *
(Type['u_k'][0] * n[0] + Type['u_k'][1] * n[1]) *
inner(p, q) * ds(mesh)))
P['F'] = A.getSubMatrix(IS[0], IS[0])
elif Type['precond'] == 'LSC':
u = TrialFunction(FS['Velocity'])
v = TestFunction(FS['Velocity'])
IS = common.IndexSet(FS)
if iter == 1:
Qdiag = PETScFunc.Assemble(assemble(inner(u, v) *
dx)).getDiagonal()
Bt = A.getSubMatrix(IS['Velocity'], IS['Pressure'])
B = A.getSubMatrix(IS['Pressure'], IS['Velocity'])
Bt.diagonalScale(Qdiag)
P['scaledBt'] = Bt
P['L'] = B * Bt
P['F'] = A.getSubMatrix(IS['Velocity'], IS['Velocity'])
else:
PrintFuncs.Errors('Navier-Stokes preconditioner has to be LSC or PCD')
P['precond'] = Type['precond']
return P
def PETScToNLiter(x,FS):
n = len(FS)
IS = common.IndexSet(FS)
u = {}
for i in range(n):
v = Function(FS.values()[i])
v.vector()[:] = x.getSubVector(IS.values()[i]).array
if FS.keys()[i] == 'Pressure':
ones = Function(FS['Pressure'])
ones.vector()[:] = 1
vv = Function(FS['Pressure'])
vv.vector()[:] = v.vector().array() - assemble(v*dx)/assemble(ones*dx)
u[FS.keys()[i]] = vv
else:
u[FS.keys()[i]] = v
return u
def NLtol(x, u, FS, Type=None):
IS = common.IndexSet(FS)
if Type == 'Update':
v = x.getSubVector(IS['Velocity']).array
p = x.getSubVector(IS['Pressure']).array
pa = Function(FS['Pressure'])
pa.vector()[:] = p
ones = Function(FS['Pressure'])
ones.vector()[:] = (0 * p + 1)
pp = Function(FS['Pressure'])
pp.vector(
)[:] = pa.vector().array() - assemble(pa * dx) / assemble(ones * dx)
vnorm = norm(v)
pnorm = norm(pp.vector().array())
V = [vnorm, pnorm]
eps = PrintFuncs.NormPrint(V, Type)
x.axpy(1.0, u)
return x, eps
else:
vcurrent = x.getSubVector(IS['Velocity']).array
pcurrent = x.getSubVector(IS['Pressure']).array
vprev = u.getSubVector(IS['Velocity']).array
pprev = u.getSubVector(IS['Pressure']).array
pa = Function(FS['Pressure'])
pa.vector()[:] = pcurrent
ones = Function(FS['Pressure'])
ones.vector()[:] = (0 * pcurrent + 1)
pp = Function(FS['Pressure'])
pp.vector(
)[:] = pa.vector().array() - assemble(pa * dx) / assemble(ones * dx)
vnorm = norm(vcurrent - vprev)
pnorm = norm(pp.vector().array() - pprev)
V = [vnorm, pnorm]
eps = PrintFuncs.NormPrint(V, Type)
return x, eps
def __init__(self, W, KSP):
self.W = W
self.IS = common.IndexSet(W)
self.KSP = KSP