def Stokes(V, Q, F, params, boundaries, domains, mesh):
parameters['reorder_dofs_serial'] = False
W = FunctionSpace(mesh, MixedElement([V, Q]))
IS = MO.IndexSet(W)
mesh = W.mesh()
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
n = FacetNormal(W.mesh())
a11 = params[2]*inner(grad(v), grad(u))*dx('everywhere')
a12 = -div(v)*p*dx('everywhere')
a21 = -div(u)*q*dx('everywhere')
a = a11+a12+a21
L = inner(v, F)*dx('everywhere') #+ inner(gradu0,v)*ds(2)
def boundary(x, on_boundary):
return on_boundary
bcu1 = DirichletBC(W.sub(0), Expression(("0.0","0.0"), degree=4), boundaries, 1)
bcu2 = DirichletBC(W.sub(0), Expression(("1.0","0.0"), degree=4), boundaries, 2)
bcu = [bcu1, bcu2]
A, b = assemble_system(a, L, bcu)
A, b = CP.Assemble(A, b)
pp = params[2]*inner(grad(v), grad(u))*dx + (1./params[2])*p*q*dx
P, Pb = assemble_system(pp, L, bcu)
P, Pb = CP.Assemble(P, Pb)
u = b.duplicate()
ksp = PETSc.KSP().create()
ksp.setTolerances(1e-8)
ksp.max_it = 200
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
ksp.setType('minres')
pc.setPythonContext(StokesPrecond.Approx(W, 1))
ksp.setOperators(A,P)
scale = b.norm()
b = b/scale
ksp.setOperators(A,A)
del A
start_time = time.time()
ksp.solve(b,u)
print ("{:40}").format("Stokes solve, time: "), " ==> ",("{:4f}").format(time.time() - start_time),("{:9}").format(" Its: "), ("{:4}").format(ksp.its), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
u = u*scale
u_k = Function(FunctionSpace(mesh, V))
p_k = Function(FunctionSpace(mesh, Q))
u_k.vector()[:] = u.getSubVector(IS[0]).array
p_k.vector()[:] = u.getSubVector(IS[1]).array
ones = Function(FunctionSpace(mesh, Q))
ones.vector()[:]=(0*ones.vector().array()+1)
p_k.vector()[:] += -assemble(p_k*dx("everywhere"))/assemble(ones*dx("everywhere"))
return u_k, p_k
def solve(A, b, u, params, Fspace, SolveType, IterType, OuterTol, InnerTol,
HiptmairMatrices, Hiptmairtol, KSPlinearfluids, Fp, kspF):
if SolveType == "Direct":
ksp = PETSc.KSP()
ksp.create(comm=PETSc.COMM_WORLD)
pc = ksp.getPC()
ksp.setType('preonly')
pc.setType('lu')
OptDB = PETSc.Options()
OptDB['pc_factor_mat_solver_package'] = "mumps"
OptDB['pc_factor_mat_ordering_type'] = "rcm"
ksp.setFromOptions()
scale = b.norm()
b = b / scale
ksp.setOperators(A, A)
del A
ksp.solve(b, u)
# Mits +=dodim
u = u * scale
MO.PrintStr("Number iterations = " + str(ksp.its), 60, "+", "\n\n",
"\n\n")
return u, ksp.its, 0
elif SolveType == "Direct-class":
ksp = PETSc.KSP()
ksp.create(comm=PETSc.COMM_WORLD)
pc = ksp.getPC()
ksp.setType('gmres')
pc.setType('none')
ksp.setFromOptions()
scale = b.norm()
b = b / scale
ksp.setOperators(A, A)
del A
ksp.solve(b, u)
# Mits +=dodim
u = u * scale
MO.PrintStr("Number iterations = " + str(ksp.its), 60, "+", "\n\n",
"\n\n")
return u, ksp.its, 0
else:
# u = b.duplicate()
if IterType == "Full":
ksp = PETSc.KSP()
ksp.create(comm=PETSc.COMM_WORLD)
pc = ksp.getPC()
ksp.setType('fgmres')
pc.setType('python')
OptDB = PETSc.Options()
OptDB['ksp_gmres_restart'] = 200
# FSpace = [Velocity,Magnetic,Pressure,Lagrange]
reshist = {}
def monitor(ksp, its, fgnorm):
reshist[its] = fgnorm
print its, " OUTER:", fgnorm
# ksp.setMonitor(monitor)
ksp.max_it = 1000
W = Fspace
FFSS = [W.sub(0), W.sub(1), W.sub(2), W.sub(3)]
pc.setPythonContext(
MHDprec.InnerOuterMAGNETICapprox(
FFSS, kspF, KSPlinearfluids[0], KSPlinearfluids[1], Fp,
HiptmairMatrices[3], HiptmairMatrices[4],
HiptmairMatrices[2], HiptmairMatrices[0],
HiptmairMatrices[1], HiptmairMatrices[6], Hiptmairtol))
#OptDB = PETSc.Options()
# OptDB['pc_factor_mat_solver_package'] = "mumps"
# OptDB['pc_factor_mat_ordering_type'] = "rcm"
# ksp.setFromOptions()
scale = b.norm()
b = b / scale
ksp.setOperators(A, A)
del A
ksp.solve(b, u)
# Mits +=dodim
u = u * scale
MO.PrintStr("Number iterations = " + str(ksp.its), 60, "+", "\n\n",
"\n\n")
return u, ksp.its, 0
IS = MO.IndexSet(Fspace, '2by2')
M_is = IS[1]
NS_is = IS[0]
kspNS = PETSc.KSP().create()
kspM = PETSc.KSP().create()
kspNS.setTolerances(OuterTol)
kspNS.setOperators(A[0])
kspM.setOperators(A[1])
# print P.symmetric
if IterType == "MD":
kspNS.setType('gmres')
kspNS.max_it = 500
pcNS = kspNS.getPC()
pcNS.setType(PETSc.PC.Type.PYTHON)
pcNS.setPythonContext(
NSpreconditioner.NSPCD(
MixedFunctionSpace([Fspace.sub(0),
Fspace.sub(1)]), kspF,
KSPlinearfluids[0], KSPlinearfluids[1], Fp))
elif IterType == "CD":
kspNS.setType('minres')
pcNS = kspNS.getPC()
pcNS.setType(PETSc.PC.Type.PYTHON)
Q = KSPlinearfluids[1].getOperators()[0]
Q = 1. / params[2] * Q
KSPlinearfluids[1].setOperators(Q, Q)
pcNS.setPythonContext(
StokesPrecond.MHDApprox(
MixedFunctionSpace([Fspace.sub(0),
Fspace.sub(1)]), kspF,
KSPlinearfluids[1]))
reshist = {}
def monitor(ksp, its, fgnorm):
reshist[its] = fgnorm
print fgnorm
# kspNS.setMonitor(monitor)
uNS = u.getSubVector(NS_is)
bNS = b.getSubVector(NS_is)
# print kspNS.view()
scale = bNS.norm()
bNS = bNS / scale
print bNS.norm()
kspNS.solve(bNS, uNS)
uNS = uNS * scale
NSits = kspNS.its
kspNS.destroy()
# for line in reshist.values():
# print line
kspM.setFromOptions()
kspM.setType(kspM.Type.MINRES)
kspM.setTolerances(InnerTol)
pcM = kspM.getPC()
pcM.setType(PETSc.PC.Type.PYTHON)
pcM.setPythonContext(
MP.Hiptmair(MixedFunctionSpace([Fspace.sub(2),
Fspace.sub(3)]),
HiptmairMatrices[3], HiptmairMatrices[4],
HiptmairMatrices[2], HiptmairMatrices[0],
HiptmairMatrices[1], HiptmairMatrices[6], Hiptmairtol))
uM = u.getSubVector(M_is)
bM = b.getSubVector(M_is)
scale = bM.norm()
bM = bM / scale
print bM.norm()
kspM.solve(bM, uM)
uM = uM * scale
Mits = kspM.its
kspM.destroy()
u = IO.arrayToVec(np.concatenate([uNS.array, uM.array]))
MO.PrintStr("Number of M iterations = " + str(Mits), 60, "+", "\n\n",
"\n\n")
MO.PrintStr("Number of NS/S iterations = " + str(NSits), 60, "+",
"\n\n", "\n\n")
return u, NSits, Mits
def Stokes(V, Q, F, u0, p0, gradu0, params, boundaries, domains, mesh):
parameters['reorder_dofs_serial'] = False
W = FunctionSpace(mesh, MixedElement([V, Q]))
IS = MO.IndexSet(W)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dx = Measure('dx', domain=mesh)
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
n = FacetNormal(W.mesh())
a11 = params[2] * inner(grad(v), grad(u)) * dx('everywhere')
a12 = -div(v) * p * dx('everywhere')
a21 = -div(u) * q * dx('everywhere')
a = a11 + a12 + a21
L = inner(v, F) * dx('everywhere') #+ inner(gradu0,v)*ds(2)
pp = params[2] * inner(grad(v),
grad(u)) * dx(0) + (1. / params[2]) * p * q * dx(0)
def boundary(x, on_boundary):
return on_boundary
# bcu = DirichletBC(W.sub(0), u0, boundaries, 1)
bcu = DirichletBC(W.sub(0), u0, boundary)
# bcu = [bcu1, bcu2]
A, b = assemble_system(a, L, bcu)
A, b = CP.Assemble(A, b)
C = A.getSubMatrix(IS[1], IS[1])
u = b.duplicate()
P, Pb = assemble_system(pp, L, bcu)
P, Pb = CP.Assemble(P, Pb)
# ksp = PETSc.KSP()
# ksp.create(comm=PETSc.COMM_WORLD)
# pc = ksp.getPC()
# ksp.setType('preonly')
# pc.setType('lu')
# OptDB = PETSc.Options()
# # if __version__ != '1.6.0':
# OptDB['pc_factor_mat_solver_package'] = "pastix"
# OptDB['pc_factor_mat_ordering_type'] = "rcm"
# ksp.setFromOptions()
# ksp.setOperators(A,A)
ksp = PETSc.KSP().create()
ksp.setTolerances(1e-8)
ksp.max_it = 200
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
ksp.setType('minres')
pc.setPythonContext(StokesPrecond.Approx(W, 1))
ksp.setOperators(A, P)
scale = b.norm()
b = b / scale
del A
start_time = time.time()
ksp.solve(b, u)
# Mits +=dodim
u = u * scale
print("{:40}").format("Stokes solve, time: "), " ==> ", (
"{:4f}").format(time.time() - start_time), (
"{:9}").format(" Its: "), ("{:4}").format(
ksp.its), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
# Mits +=dodim
u_k = Function(FunctionSpace(mesh, V))
p_k = Function(FunctionSpace(mesh, Q))
u_k.vector()[:] = u.getSubVector(IS[0]).array
p_k.vector()[:] = u.getSubVector(IS[1]).array
ones = Function(FunctionSpace(mesh, Q))
ones.vector()[:] = (0 * ones.vector().array() + 1)
p_k.vector()[:] += -assemble(p_k * dx('everywhere')) / assemble(
ones * dx('everywhere'))
return u_k, p_k
# pc = ksp.getPC()
# ksp.setType('minres')
# pc.setType('lu')
# OptDB = PETSc.Options()
# # if __version__ != '1.6.0':
# # OptDB['pc_factor_mat_solver_package'] = "umfpack"
# # OptDB['pc_factor_mat_ordering_type'] = "rcm"
# ksp.setFromOptions()
ksp = PETSc.KSP().create()
ksp.setTolerances(1e-8)
ksp.max_it = 200
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
ksp.setType('minres')
pc.setPythonContext(StokesPrecond.Approx(W, 1))
scale = b.norm()
b = b / scale
ksp.setOperators(A, P)
del A
start_time = time.time()
ksp.solve(b, x)
print("{:40}").format("Stokes solve, time: "), " ==> ", (
"{:4f}").format(time.time() - start_time), (
"{:9}").format(" Its: "), ("{:4}").format(
ksp.its), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
x = x * scale
b_k = Function(Velocity)
r_k = Function(Pressure)
def Stokes(V, Q, F, u0, pN, params, boundaries, domains):
parameters['reorder_dofs_serial'] = False
W = V * Q
IS = MO.IndexSet(W)
mesh = W.mesh()
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dx = Measure('dx', domain=mesh)
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
n = FacetNormal(W.mesh())
a11 = params[2] * inner(grad(v), grad(u)) * dx('everywhere')
a12 = -div(v) * p * dx('everywhere')
a21 = -div(u) * q * dx('everywhere')
a = a11 + a12 + a21
L = inner(v, F) * dx('everywhere') #+ inner(pN*n,v)*ds(1)
pp = params[2] * inner(grad(v), grad(u)) * dx('everywhere') + (
1. / params[2]) * p * q * dx('everywhere')
def boundary(x, on_boundary):
return on_boundary
bcu = DirichletBC(W.sub(0), u0, boundary)
#bcr = DirichletBC(W.sub(1), Expression(("0.0")), boundary)
A, b = assemble_system(a, L, bcu)
A, b = CP.Assemble(A, b)
C = A.getSubMatrix(IS[1], IS[1])
u = b.duplicate()
P, Pb = assemble_system(pp, L, bcu)
# MO.StoreMatrix(P.sparray(),"P"+str(W.dim()))
P = CP.Assemble(P)
M = P.getSubMatrix(IS[1], IS[1])
# print M
# ksp = PETSc.KSP()
# ksp.create(comm=PETSc.COMM_WORLD)
# pc = ksp.getPC()
# ksp.setType('preonly')
# pc.setType('lu')
# OptDB = PETSc.Options()
# if __version__ != '1.6.0':
# OptDB['pc_factor_mat_solver_package'] = "mumps"
# OptDB['pc_factor_mat_ordering_type'] = "rcm"
# ksp.setFromOptions()
# ksp.setOperators(A,A)
ksp = PETSc.KSP().create()
pc = ksp.getPC()
ksp.setType(ksp.Type.MINRES)
ksp.setTolerances(1e-8)
ksp.max_it = 500
#ksp.max_it = 2
pc.setType(PETSc.PC.Type.PYTHON)
pc.setPythonContext(SP.Approx(W, M))
ksp.setOperators(A, P)
scale = b.norm()
b = b / scale
del A
start_time = time.time()
ksp.solve(b, u)
print 333
# Mits +=dodim
u = u * scale
print("{:40}").format("Stokes solve, time: "), " ==> ", (
"{:4f}").format(time.time() - start_time), (
"{:9}").format(" Its: "), ("{:4}").format(
ksp.its), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
u_k = Function(V)
p_k = Function(Q)
u_k.vector()[:] = u.getSubVector(IS[0]).array
p_k.vector()[:] = u.getSubVector(IS[1]).array
# ones = Function(Q)
# ones.vector()[:]=(0*ones.vector().array()+1)
# p_k.vector()[:] += -assemble(p_k*dx('everywhere'))/assemble(ones*dx('everywhere'))
return u_k, p_k
def solve(A,b,u,IS,Fspace,IterType,OuterTol,InnerTol,HiptmairMatrices,KSPlinearfluids,kspF,Fp,MatrixLinearFluids,kspFp):
if IterType == "Full":
kspOuter = PETSc.KSP().create()
kspOuter.setTolerances(OuterTol)
kspOuter.setType('fgmres')
u_is = PETSc.IS().createGeneral(range(Fspace[0].dim()))
p_is = PETSc.IS().createGeneral(range(Fspace[0].dim(),Fspace[0].dim()+Fspace[1].dim()))
Bt = A.getSubMatrix(u_is,p_is)
reshist = {}
def monitor(ksp, its, fgnorm):
reshist[its] = fgnorm
print "OUTER:", fgnorm
kspOuter.setMonitor(monitor)
pcOutter = kspOuter.getPC()
pcOutter.setType(PETSc.PC.Type.KSP)
kspOuter.setOperators(A,A)
kspOuter.max_it = 500
kspInner = pcOutter.getKSP()
kspInner.max_it = 100
kspInner.max_it = 100
reshist1 = {}
def monitor(ksp, its, fgnorm):
reshist1[its] = fgnorm
print "INNER:", fgnorm
# kspInner.setMonitor(monitor)
kspInner.setType('gmres')
kspInner.setTolerances(InnerTol)
pcInner = kspInner.getPC()
pcInner.setType(PETSc.PC.Type.PYTHON)
pcInner.setPythonContext(MHDstabPrecond.InnerOuterWITHOUT(Fspace,kspF, KSPlinearfluids[0], KSPlinearfluids[1],Fp, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],1e-6,A))
PP = PETSc.Mat().createPython([A.size[0], A.size[0]])
PP.setType('python')
p = PrecondMulti.MultiApply(Fspace,A,HiptmairMatrices[6],MatrixLinearFluids[1],MatrixLinearFluids[0],kspFp, HiptmairMatrices[3])
PP.setPythonContext(p)
kspInner.setOperators(PP)
tic()
scale = b.norm()
b = b/scale
print b.norm()
kspOuter.solve(b, u)
u = u*scale
print toc()
# print s.getvalue()
NSits = kspOuter.its
del kspOuter
Mits = kspInner.its
del kspInner
# print u.array
return u,NSits,Mits
NS_is = IS[0]
M_is = IS[1]
kspNS = PETSc.KSP().create()
kspM = PETSc.KSP().create()
kspNS.setTolerances(OuterTol)
kspNS.setOperators(A.getSubMatrix(NS_is,NS_is))
kspM.setOperators(A.getSubMatrix(M_is,M_is))
del A
uNS = u.getSubVector(NS_is)
bNS = b.getSubVector(NS_is)
kspNS.setType('gmres')
pcNS = kspNS.getPC()
kspNS.setTolerances(OuterTol)
pcNS.setType(PETSc.PC.Type.PYTHON)
if IterType == "MD":
pcNS.setPythonContext(NSpreconditioner.NSPCD(MixedFunctionSpace([Fspace[0],Fspace[1]]), kspF, KSPlinearfluids[0], KSPlinearfluids[1],Fp))
else:
pcNS.setPythonContext(StokesPrecond.MHDApprox(MixedFunctionSpace([Fspace[0],Fspace[1]]), kspF, KSPlinearfluids[1]))
scale = bNS.norm()
bNS = bNS/scale
start_time = time.time()
kspNS.solve(bNS, uNS)
print ("{:25}").format("NS, time: "), " ==> ",("{:4f}").format(time.time() - start_time),("{:9}").format(" Its: "), ("{:4}").format(kspNS.its), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
uNS = scale*uNS
NSits = kspNS.its
# kspNS.destroy()
# for line in reshist.values():
# print line
kspM.setFromOptions()
kspM.setType(kspM.Type.MINRES)
kspM.setTolerances(InnerTol)
pcM = kspM.getPC()
pcM.setType(PETSc.PC.Type.PYTHON)
pcM.setPythonContext(MP.Hiptmair(MixedFunctionSpace([Fspace[2],Fspace[3]]), HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],1e-6))
# x = x*scale
uM = u.getSubVector(M_is)
bM = b.getSubVector(M_is)
scale = bM.norm()
bM = bM/scale
start_time = time.time()
kspM.solve(bM, uM)
print ("{:25}").format("Maxwell solve, time: "), " ==> ",("{:4f}").format(time.time() - start_time),("{:9}").format(" Its: "), ("{:4}").format(kspM.its), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
uM = uM*scale
Mits = kspM.its
kspM.destroy()
u = IO.arrayToVec(np.concatenate([uNS.array, uM.array]))
return u,NSits,Mits
def solve(A,
b,
u,
P,
IS,
Fspace,
IterType,
OuterTol,
InnerTol,
Mass=0,
L=0,
F=0):
# u = b.duplicate()
if IterType == "Full":
kspOuter = PETSc.KSP().create()
kspOuter.setTolerances(OuterTol)
kspOuter.setType('fgmres')
reshist = {}
def monitor(ksp, its, fgnorm):
reshist[its] = fgnorm
print "OUTER:", fgnorm
kspOuter.setMonitor(monitor)
pcOutter = kspOuter.getPC()
pcOutter.setType(PETSc.PC.Type.KSP)
kspOuter.setOperators(A)
kspOuter.max_it = 500
kspInner = pcOutter.getKSP()
kspInner.max_it = 100
reshist1 = {}
def monitor(ksp, its, fgnorm):
reshist1[its] = fgnorm
print "INNER:", fgnorm
# kspInner.setMonitor(monitor)
kspInner.setType('gmres')
kspInner.setTolerances(InnerTol)
pcInner = kspInner.getPC()
pcInner.setType(PETSc.PC.Type.PYTHON)
pcInner.setPythonContext(MHDprecond.D(Fspace, P, Mass, F, L))
PP = PETSc.Mat().createPython([A.size[0], A.size[0]])
PP.setType('python')
p = PrecondMulti.P(Fspace, P, Mass, L, F)
PP.setPythonContext(p)
kspInner.setOperators(PP)
tic()
scale = b.norm()
b = b / scale
print b.norm()
kspOuter.solve(b, u)
u = u * scale
print toc()
# print s.getvalue()
NSits = kspOuter.its
del kspOuter
Mits = kspInner.its
del kspInner
# print u.array
return u, NSits, Mits
NS_is = IS[0]
M_is = IS[1]
kspNS = PETSc.KSP().create()
kspM = PETSc.KSP().create()
kspNS.setTolerances(OuterTol)
kspNS.setOperators(A.getSubMatrix(NS_is, NS_is),
P.getSubMatrix(NS_is, NS_is))
kspM.setOperators(A.getSubMatrix(M_is, M_is), P.getSubMatrix(M_is, M_is))
# print P.symmetric
A.destroy()
P.destroy()
if IterType == "MD":
kspNS.setType('gmres')
kspNS.max_it = 500
pcNS = kspNS.getPC()
pcNS.setType(PETSc.PC.Type.PYTHON)
pcNS.setPythonContext(
NSprecond.PCDdirect(MixedFunctionSpace([Fspace[0], Fspace[1]]),
Mass, F, L))
elif IterType == "CD":
kspNS.setType('minres')
pcNS = kspNS.getPC()
pcNS.setType(PETSc.PC.Type.PYTHON)
pcNS.setPythonContext(
StokesPrecond.Approx(MixedFunctionSpace([Fspace[0], Fspace[1]])))
reshist = {}
def monitor(ksp, its, fgnorm):
reshist[its] = fgnorm
print fgnorm
# kspNS.setMonitor(monitor)
uNS = u.getSubVector(NS_is)
bNS = b.getSubVector(NS_is)
# print kspNS.view()
scale = bNS.norm()
bNS = bNS / scale
print bNS.norm()
kspNS.solve(bNS, uNS)
uNS = uNS * scale
NSits = kspNS.its
kspNS.destroy()
# for line in reshist.values():
# print line
kspM.setFromOptions()
kspM.setType(kspM.Type.MINRES)
kspM.setTolerances(InnerTol)
pcM = kspM.getPC()
pcM.setType(PETSc.PC.Type.PYTHON)
pcM.setPythonContext(MP.Direct(MixedFunctionSpace([Fspace[2], Fspace[3]])))
uM = u.getSubVector(M_is)
bM = b.getSubVector(M_is)
scale = bM.norm()
bM = bM / scale
print bM.norm()
kspM.solve(bM, uM)
uM = uM * scale
Mits = kspM.its
kspM.destroy()
u = IO.arrayToVec(np.concatenate([uNS.array, uM.array]))
return u, NSits, Mits
def Stokes(V, Q, BC, f, params, FS, InitialTol, Neumann=None, A=0, b=0):
if A == 0:
# parameters['linear_algebra_backend'] = 'uBLAS'
# parameters = CP.ParameterSetup()
# parameters["form_compiler"]["quadrature_degree"] = 6
parameters['reorder_dofs_serial'] = False
Split = 'No'
if Split == 'No':
W = V * Q
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
print FS
def boundary(x, on_boundary):
return on_boundary
bcu = DirichletBC(W.sub(0), BC, boundary)
u_k = Function(V)
if FS == "DG":
h = CellSize(V.mesh())
h_avg = avg(h)
a11 = inner(grad(v), grad(u)) * dx
a12 = div(v) * p * dx
a21 = div(u) * q * dx
a22 = 0.1 * h_avg * jump(p) * jump(q) * dS
L1 = inner(v, f) * dx
a = params[2] * a11 - a12 - a21 - a22
else:
if W.sub(0).__str__().find("Bubble") == -1 and W.sub(
0).__str__().find("CG1") != -1:
print "Bubble Bubble Bubble Bubble Bubble"
a11 = inner(grad(v), grad(u)) * dx
a12 = div(v) * p * dx
a21 = div(u) * q * dx
h = CellSize(V.mesh())
beta = 0.2
delta = beta * h * h
a22 = delta * inner(grad(p), grad(q)) * dx
a = params[2] * a11 - a12 - a21 - a22
L1 = inner(v - delta * grad(q), f) * dx
else:
a11 = inner(grad(v), grad(u)) * dx
a12 = div(v) * p * dx
a21 = div(u) * q * dx
L1 = inner(v, f) * dx
a = params[2] * a11 - a12 - a21
tic()
AA, bb = assemble_system(a, L1, bcu)
A, b = CP.Assemble(AA, bb)
del AA
x = b.duplicate()
pp = params[2] * inner(
grad(v), grad(u)) * dx + (1. / params[2]) * p * q * dx
PP, Pb = assemble_system(pp, L1, bcu)
P = CP.Assemble(PP)
del PP
else:
u = TrialFunction(V)
v = TestFunction(V)
p = TrialFunction(Q)
q = TestFunction(Q)
def boundary(x, on_boundary):
return on_boundary
W = V * Q
bcu = DirichletBC(V, BC, boundary)
u_k = Function(V)
if FS == "DG":
h = CellSize(V.mesh())
h_avg = avg(h)
a11 = inner(grad(v), grad(u)) * dx
a12 = div(v) * p * dx
a21 = div(u) * q * dx
a22 = 0.1 * h_avg * jump(p) * jump(q) * dS
L1 = inner(v, f) * dx
else:
if V.__str__().find(
"Bubble") == -1 and V.__str__().find("CG1") != -1:
a11 = params[2] * inner(grad(v), grad(u)) * dx
a12 = -div(v) * p * dx
a21 = div(u) * q * dx
L1 = inner(v, f) * dx
h = CellSize(V.mesh())
beta = 0.2
delta = beta * h * h
a22 = delta * inner(grad(p), grad(q)) * dx
else:
a11 = params[2] * inner(grad(v), grad(u)) * dx
a12 = -div(v) * p * dx
a21 = div(u) * q * dx
L1 = inner(v, f) * dx
AA = assemble(a11)
bcu.apply(AA)
b = assemble(L1)
bcu.apply(b)
AA, b = assemble_system(a11, L1, bcu)
BB = assemble(a12)
AAA = AA
AA = AA.sparray()
mesh = V.mesh()
dim = mesh.geometry().dim()
LagrangeBoundary = np.zeros(dim * mesh.num_vertices())
Row = (AA.sum(0)[0, :dim * mesh.num_vertices()] -
AA.diagonal()[:dim * mesh.num_vertices()])
VelocityBoundary = np.abs(Row.A1) > 1e-4
LagrangeBoundary[VelocityBoundary] = 1
BubbleDOF = np.ones(dim * mesh.num_cells())
VelocityBoundary = np.concatenate((LagrangeBoundary, BubbleDOF),
axis=1)
BC = sp.spdiags(VelocityBoundary, 0, V.dim(), V.dim())
B = BB.sparray().T * BC
A = CP.Scipy2PETSc(sp.bmat([[AA, B.T], [B, None]]))
io.savemat("A.mat", {"A": sp.bmat([[AA, B.T], [B, None]])})
b = IO.arrayToVec(
np.concatenate((b.array(), np.zeros(Q.dim())), axis=0))
mass = (1. / params[2]) * p * q * dx
mass1 = assemble(mass).sparray()
mass2 = assemble(mass)
W = V * Q
io.savemat("P.mat", {"P": sp.bmat([[AA, None], [None, (mass1)]])})
P = CP.Scipy2PETSc(sp.bmat([[AA, None], [None, (mass1)]]))
else:
W = V * Q
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
print FS
def boundary(x, on_boundary):
return on_boundary
bcu = DirichletBC(W.sub(0), BC, boundary)
u_k = Function(V)
pp = params[2] * inner(grad(v),
grad(u)) * dx + (1. / params[2]) * p * q * dx
P = assemble(pp)
bcu.apply(P)
P = CP.Assemble(P)
ksp = PETSc.KSP().create()
pc = ksp.getPC()
ksp.setType(ksp.Type.MINRES)
ksp.setTolerances(InitialTol)
pc.setType(PETSc.PC.Type.PYTHON)
if Split == "Yes":
A = PETSc.Mat().createPython([W.dim(), W.dim()])
A.setType('python')
print AAA
a = MM.Mat2x2multi(W, [CP.Assemble(AAA), CP.Scipy2PETSc(B)])
A.setPythonContext(a)
pc.setPythonContext(
SP.ApproxSplit(W, CP.Assemble(AAA), CP.Assemble(mass2)))
else:
pc.setPythonContext(SP.Approx(W, P))
ksp.setOperators(A, P)
x = b.duplicate()
tic()
ksp.solve(b, x)
print("{:40}").format("Stokes solve, time: "), " ==> ", ("{:4f}").format(
toc()), ("{:9}").format(" Its: "), ("{:4}").format(
ksp.its), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
X = x.array
print np.linalg.norm(x)
# print X
ksp.destroy()
x = X[0:V.dim()]
p = X[V.dim():]
# x =
u = Function(V)
u.vector()[:] = x
# print u.vector().array()
pp = Function(Q)
n = p.shape
pp.vector()[:] = p
ones = Function(Q)
ones.vector()[:] = (0 * ones.vector().array() + 1)
pp.vector()[:] += -assemble(pp * dx) / assemble(ones * dx)
#
# PP = io.loadmat('Ptrue.mat')["Ptrue"]
# PP = CP.Scipy2PETSc(PP)
# x = IO.arrayToVec(np.random.rand(W.dim()))
# y = x.duplicate()
# yy = x.duplicate()
# SP.ApproxFunc(W,PP,x,y)
# SP.ApproxSplitFunc(W,CP.Scipy2PETSc(AA),CP.Scipy2PETSc(mass),x,yy)
# print np.linalg.norm(y.array-yy.array)
# sssss
return u, pp
