def create(self, pc):
self.diag = None
kspNS = PETSc.KSP()
kspNS.create(comm=PETSc.COMM_WORLD)
pcNS = kspNS.getPC()
kspNS.setType('gmres')
pcNS.setType('python')
pcNS.setPythonContext(
NSprecond.PCDdirect(
MixedFunctionSpace([self.Fspace[0], self.Fspace[1]]), self.Q,
self.F, self.L))
kspNS.setTolerances(1e-3)
kspNS.setFromOptions()
self.kspNS = kspNS
kspM = PETSc.KSP()
kspM.create(comm=PETSc.COMM_WORLD)
pcM = kspM.getPC()
kspM.setType('gmres')
pcM.setType('python')
kspM.setTolerances(1e-3)
pcM.setPythonContext(
MP.Direct(MixedFunctionSpace([self.Fspace[2], self.Fspace[3]])))
kspM.setFromOptions()
self.kspM = kspM
def Maxwell(V, Q, F, params, HiptmairMatrices, Hiptmairtol, mesh):
parameters['reorder_dofs_serial'] = False
W = FunctionSpace(mesh, MixedElement([V, Q]))
IS = MO.IndexSet(W)
print params
(b, r) = TrialFunctions(W)
(c, s) = TestFunctions(W)
a11 = params[1]*params[2]*inner(curl(b), curl(c))*dx('everywhere')
a21 = inner(b,grad(s))*dx('everywhere')
a12 = inner(c,grad(r))*dx('everywhere')
L = inner(c, F)*dx('everywhere')
a = a11+a12+a21
def boundary(x, on_boundary):
return on_boundary
bcb = DirichletBC(W.sub(0), Expression(("1.0","0.0"), degree=4), boundary)
bcr = DirichletBC(W.sub(1), Expression(("0.0"), degree=4), boundary)
bc = [bcb, bcr]
A, b = assemble_system(a, L, bc)
A, b = CP.Assemble(A, b)
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(MP.Hiptmair(W, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],Hiptmairtol))
scale = b.norm()
b = b/scale
ksp.setOperators(A,A)
del A
start_time = time.time()
ksp.solve(b,u)
print ("{:40}").format("Maxwell 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
b_k = Function(FunctionSpace(mesh, V))
r_k = Function(FunctionSpace(mesh, Q))
b_k.vector()[:] = u.getSubVector(IS[0]).array
r_k.vector()[:] = u.getSubVector(IS[1]).array
return b_k, r_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
p22 = inner(grad(p), grad(q)) * dx
pp = p11 + p22
PP, Pb = assemble_system(pp, L1, bcs)
P = CP.Assemble(PP)
if (Solving == 'Direct'):
ksp = PETSc.KSP().create()
ksp.setOperators(A)
ksp.setFromOptions()
ksp.setType(ksp.Type.MINRES)
ksp.setTolerances(1e-8)
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
pc.setPythonContext(MP.Approx(W, P))
# print 'Solving with:', ksp.getType()
# Solve!
tic()
ksp.solve(bb, x)
SolTime[xx - 1] = toc()
print "time to solve: ", SolTime[xx - 1]
OuterIt[xx - 1] = ksp.its
r = bb.duplicate()
A.mult(x, r)
r.aypx(-1, bb)
rnorm = r.norm()
PETSc.Sys.Print('error norm = %g' % rnorm, comm=PETSc.COMM_WORLD)
del A, P
Hiptmairtol = 1e-3
tic()
kspVector, kspScalar, kspCGScalar, diag = HiptmairSetup.HiptmairKSPsetup(VectorLaplacian, ScalarLaplacian, Prec, CGtol)
del A, VectorLaplacian, ScalarLaplacian
print ("{:40}").format("Hiptmair Setup time:"), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
reshist = {}
def monitor(ksp, its, rnorm):
print rnorm
reshist[its] = rnorm
ksp.setMonitor(monitor)
pc.setPythonContext(MaxwellPrecond.Hiptmair(W, kspScalar, kspCGScalar, kspVector, G, P, Prec,Hiptmairtol))
scale = b.norm()
b = b/scale
start_time = time.time()
ksp.solve(b, x)
TimeSave[xx-1] = time.time() - start_time
x = x*scale
print ksp.its
print TimeSave[xx-1]
ItsSave[xx-1] = len(reshist)
CGits, Hits, CGtime, HiptmairTime = pc.getPythonContext().ITS()
ItsHipt[xx-1] =float(Hits)/len(reshist)
ItsCG[xx-1] =float(CGits)/len(reshist)
print " \n\n\n\n"
Ve = FunctionSpace(mesh,"N1curl",2)
def Maxwell(V, Q, F, b0, r0, params, boundaries, HiptmairMatrices,
Hiptmairtol):
parameters['reorder_dofs_serial'] = False
W = V * Q
IS = MO.IndexSet(W)
(b, r) = TrialFunctions(W)
(c, s) = TestFunctions(W)
a11 = params[1] * params[2] * inner(curl(b), curl(c)) * dx('everywhere')
a21 = inner(b, grad(s)) * dx('everywhere')
a12 = inner(c, grad(r)) * dx('everywhere')
L = inner(c, F) * dx('everywhere')
a = a11 + a12 + a21
def boundary(x, on_boundary):
return on_boundary
bcb = DirichletBC(W.sub(0), b0, boundary)
bcr = DirichletBC(W.sub(1), r0, boundary)
bc = [bcb, bcr]
A, b = assemble_system(a, L, bc)
A, b = CP.Assemble(A, b)
u = b.duplicate()
# 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 = 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(
MP.Hiptmair(W, HiptmairMatrices[3], HiptmairMatrices[4],
HiptmairMatrices[2], HiptmairMatrices[0],
HiptmairMatrices[1], HiptmairMatrices[6], Hiptmairtol))
scale = b.norm()
b = b / scale
ksp.setOperators(A, A)
del A
start_time = time.time()
ksp.solve(b, u)
print("{:40}").format("Maxwell 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
b_k = Function(V)
r_k = Function(Q)
b_k.vector()[:] = u.getSubVector(IS[0]).array
r_k.vector()[:] = u.getSubVector(IS[1]).array
return b_k, r_k
def Maxwell(V, Q, F, b0, r0, params, mesh, HiptmairMatrices, Hiptmairtol):
parameters['reorder_dofs_serial'] = False
W = V * Q
W = FunctionSpace(mesh, MixedElement([V, Q]))
IS = MO.IndexSet(W)
(b, r) = TrialFunctions(W)
(c, s) = TestFunctions(W)
if params[0] == 0.0:
a11 = params[1] * inner(curl(b), curl(c)) * dx
else:
a11 = params[1] * params[0] * inner(curl(b), curl(c)) * dx
a21 = inner(b, grad(s)) * dx
a12 = inner(c, grad(r)) * dx
# print F
L = inner(c, F) * dx
a = a11 + a12 + a21
def boundary(x, on_boundary):
return on_boundary
# class b0(Expression):
# def __init__(self):
# self.p = 1
# def eval_cell(self, values, x, ufc_cell):
# values[0] = 0.0
# values[1] = 1.0
# def value_shape(self):
# return (2,)
bcb = DirichletBC(W.sub(0), b0, boundary)
bcr = DirichletBC(W.sub(1), r0, boundary)
bc = [bcb, bcr]
A, b = assemble_system(a, L, bc)
A, b = CP.Assemble(A, b)
u = b.duplicate()
# 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'] = "pastix"
# 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(
MP.Hiptmair(W, HiptmairMatrices[3], HiptmairMatrices[4],
HiptmairMatrices[2], HiptmairMatrices[0],
HiptmairMatrices[1], HiptmairMatrices[6], Hiptmairtol))
scale = b.norm()
b = b / scale
ksp.setOperators(A, A)
del A
start_time = time.time()
ksp.solve(b, u)
print("{:40}").format("Maxwell 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
b_k = Function(FunctionSpace(mesh, V))
r_k = Function(FunctionSpace(mesh, Q))
b_k.vector()[:] = u.getSubVector(IS[0]).array
r_k.vector()[:] = u.getSubVector(IS[1]).array
return b_k, r_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
pcNS.setType(PETSc.PC.Type.LU)
uNS = u.getSubVector(NS_is)
bNS = b.getSubVector(NS_is)
kspNS.solve(bNS, uNS)
NSits = kspNS.its
kspNS.destroy()
kspM.setFromOptions()
kspM.setType(kspM.Type.MINRES)
kspM.setTolerances(1e-5)
pcM = kspM.getPC()
pcM.setType(PETSc.PC.Type.PYTHON)
pcM.setPythonContext(MP.Direct(MixedFunctionSpace([FSpaces[2],FSpaces[3]])))
uM = u.getSubVector(M_is)
bM = b.getSubVector(M_is)
kspM.solve(bM, uM)
Mits = kspM.its
kspM.destroy()
u = IO.arrayToVec(np.concatenate([uNS.array, uM.array]))
print NSits
print Mits
tic()
# ksp.solve(b, u)
time = toc()
print time
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
pcNS = kspNS.getPC()
pcNS.setType(PETSc.PC.Type.PYTHON)
pcNS.setPythonContext(NSprecond.PCDdirect(MixedFunctionSpace([Velocity,Pressure]), A.getSubMatrix(NS_is,NS_is), Mass, fp, L))
kspNS.setOperators(A.getSubMatrix(NS_is,NS_is))
uNS = u.getSubVector(NS_is)
bNS = b.getSubVector(NS_is)
kspNS.solve(bNS, uNS)
print kspNS.its
kspM.setFromOptions()
kspM.setType(kspM.Type.MINRES)
kspM.setTolerances(1e-6)
pcM = kspM.getPC()
pcM.setType(PETSc.PC.Type.PYTHON)
pcM.setPythonContext(MP.Direct(MixedFunctionSpace([Magnetic,Lagrange]),P.getSubMatrix(M_is,M_is)))
kspM.setOperators(A.getSubMatrix(M_is,M_is))
uM = u.getSubVector(M_is)
bM = b.getSubVector(M_is)
kspM.solve(bM, uM)
print kspM.its
time = toc()
u = IO.arrayToVec(np.concatenate([uNS.array, uM.array]))
print time
SolutionTime = SolutionTime +time
# OptDB = PETSc.Options()
# # OptDB["ksp_type"] = "gmres"
# # OptDB["pc_type"] = "ilu"
# # OptDB["pc_factor_shift_amount"] = .1
def Maxwell(u,
V,
Q,
BC,
f,
params,
HiptmairMatrices,
Hiptmairtol,
InitialTol,
Neumann=None):
# parameters['linear_algebra_backend'] = 'uBLAS'
dim = f.shape()[0]
W = V * Q
(b, r) = TrialFunctions(W)
(c, s) = TestFunctions(W)
def boundary(x, on_boundary):
return on_boundary
bcb = DirichletBC(W.sub(0), BC[0], boundary)
bcr = DirichletBC(W.sub(1), BC[1], boundary)
if params[0] == 0:
a11 = params[1] * inner(curl(c), curl(b)) * dx
else:
if dim == 2:
a11 = params[1] * params[0] * inner(curl(c), curl(b)) * dx
elif dim == 3:
a11 = params[1] * params[0] * inner(curl(c), curl(b)) * dx
a12 = inner(c, grad(r)) * dx
a21 = inner(b, grad(s)) * dx
Lmaxwell = inner(c, f) * dx
maxwell = a11 + a12 + a21
bcs = [bcb, bcr]
tic()
AA, bb = assemble_system(maxwell, Lmaxwell, bcs)
A, bb = CP.Assemble(AA, bb)
del AA
x = bb.duplicate()
u_is = PETSc.IS().createGeneral(range(V.dim()))
p_is = PETSc.IS().createGeneral(range(V.dim(), V.dim() + Q.dim()))
ksp = PETSc.KSP().create()
ksp.setTolerances(InitialTol)
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
# ksp.setType('preonly')
# pc.setType('lu')
# [G, P, kspVector, kspScalar, kspCGScalar, diag]
reshist = {}
def monitor(ksp, its, rnorm):
print rnorm
reshist[its] = rnorm
# ksp.setMonitor(monitor)
if V.__str__().find("N1curl2") == -1:
ksp.setOperators(A)
pc.setPythonContext(
MP.Hiptmair(W, HiptmairMatrices[3], HiptmairMatrices[4],
HiptmairMatrices[2], HiptmairMatrices[0],
HiptmairMatrices[1], HiptmairMatrices[6], Hiptmairtol))
else:
p = params[1] * params[0] * inner(curl(c), curl(b)) * dx + inner(
c, b) * dx + inner(grad(r), grad(s)) * dx
P = assemble(p)
for bc in bcs:
bc.apply(P)
P = CP.Assemble(P)
ksp.setOperators(A, P)
pc.setType(PETSc.PC.Type.LU)
# pc.setPythonContext(MP.Direct(W))
scale = bb.norm()
bb = bb / scale
start_time = time.time()
ksp.solve(bb, x)
print("{:40}").format("Maxwell 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
ksp.destroy()
X = IO.vecToArray(x)
x = X[0:V.dim()]
ua = Function(V)
ua.vector()[:] = x
p = X[V.dim():]
pa = Function(Q)
pa.vector()[:] = p
del ksp, pc
return ua, pa