def ams(singular=False, **kwargs):
prc = kwargs.pop('prc')
blockname = kwargs.pop('blockname')
print_level = kwargs.pop('print_level', -1)
row = prc.get_row_by_name(blockname)
col = prc.get_col_by_name(blockname)
mat = prc.get_operator_block(row, col)
fes = prc.get_test_fespace(blockname)
inv_ams = mfem.HypreAMS(mat, fes)
if singular:
inv_ams.SetSingularProblem()
inv_ams.SetPrintLevel(print_level)
inv_ams.iterative_mode = False
return inv_ams
# 11. Set up a block-diagonal preconditioner for the 2x2 normal equation
#
# [ S0^{-1} 0 ]
# [ 0 Shat^{-1} ] Shat = (Bhat^T Sinv Bhat)
#
# corresponding to the primal (x0) and interfacial (xhat) unknowns.
# Since the Shat operator is equivalent to an H(div) matrix reduced to
# the interfacial skeleton, we approximate its inverse with one V-cycle
# of the ADS preconditioner from the hypre library (in 2D we use AMS for
# the rotated H(curl) problem).
S0inv = mfem.HypreBoomerAMG(matS0)
S0inv.SetPrintLevel(0)
Shat = mfem.RAP(matSinv, matBhat)
if (dim == 2): Shatinv = mfem.HypreAMS(Shat, xhat_space)
else: Shatinv = mfem.HypreADS(Shat, xhat_space)
P = mfem.BlockDiagonalPreconditioner(true_offsets)
P.SetDiagonalBlock(0, S0inv)
P.SetDiagonalBlock(1, Shatinv)
# 12. Solve the normal equation system using the PCG iterative solver.
# Check the weighted norm of residual for the DPG least square problem.
# Wrap the primal variable in a GridFunction for visualization purposes.
pcg = mfem.CGSolver(MPI.COMM_WORLD)
pcg.SetOperator(A)
pcg.SetPreconditioner(P)
pcg.SetRelTol(1e-6)
pcg.SetMaxIter(200)
pcg.SetPrintLevel(1)
a.Assemble() a.EliminateEssentialBCDiag(ess_bdr, 1.0) a.Finalize() m = mfem.ParBilinearForm(fespace) m.AddDomainIntegrator(mfem.VectorFEMassIntegrator(one)) m.Assemble() # shift the eigenvalue corresponding to eliminated dofs to a large value m.EliminateEssentialBCDiag(ess_bdr, 2.3e-308) m.Finalize() A = a.ParallelAssemble() M = m.ParallelAssemble() ams = mfem.HypreAMS(A, fespace) ams.SetPrintLevel(0) ams.SetSingularProblem() ame = mfem.HypreAME(MPI.COMM_WORLD) ame.SetNumModes(nev) ame.SetPreconditioner(ams) ame.SetMaxIter(100) ame.SetTol(1e-8) ame.SetPrintLevel(1) ame.SetMassMatrix(M) ame.SetOperator(A) eigenvalues = doubleArray() ame.Solve() ame.GetEigenvalues(eigenvalues)
def solve_parallel(self, A, b, x=None):
from mpi4py import MPI
myid = MPI.COMM_WORLD.rank
nproc = MPI.COMM_WORLD.size
from petram.helper.mpi_recipes import gather_vector
def get_block(Op, i, j):
try:
return Op._linked_op[(i, j)]
except KeyError:
return None
offset = A.RowOffsets()
rows = A.NumRowBlocks()
cols = A.NumColBlocks()
if self.gui.write_mat:
for i in range(cols):
for j in range(rows):
m = get_block(A, i, j)
if m is None: continue
m.Print('matrix_' + str(i) + '_' + str(j))
for i, bb in enumerate(b):
for j in range(rows):
v = bb.GetBlock(j)
v.Print('rhs_' + str(i) + '_' + str(j) + '.' + smyid)
if x is not None:
for j in range(rows):
xx = x.GetBlock(j)
xx.Print('x_' + str(i) + '_' + str(j) + '.' + smyid)
M = mfem.BlockDiagonalPreconditioner(offset)
prcs = dict(self.gui.preconditioners)
name = self.Aname
assert not self.gui.parent.is_complex(), "can not solve complex"
if self.gui.parent.is_converted_from_complex():
name = sum([[n, n] for n in name], [])
for k, n in enumerate(name):
prc = prcs[n][1]
if prc == "None": continue
name = "".join([tmp for tmp in prc if not tmp.isdigit()])
A0 = get_block(A, k, k)
if A0 is None and not name.startswith('schur'): continue
if hasattr(mfem.HypreSmoother, prc):
invA0 = mfem.HypreSmoother(A0)
invA0.SetType(getattr(mfem.HypreSmoother, prc))
elif prc == 'ams':
depvar = self.engine.r_dep_vars[k]
dprint1("setting up AMS for ", depvar)
prec_fespace = self.engine.fespaces[depvar]
invA0 = mfem.HypreAMS(A0, prec_fespace)
invA0.SetSingularProblem()
elif name == 'MUMPS':
cls = SparseSmootherCls[name][0]
invA0 = cls(A0, gui=self.gui[prc], engine=self.engine)
elif name.startswith('schur'):
args = name.split("(")[-1].split(")")[0].split(",")
dprint1("setting up schur for ", args)
if len(args) > 1:
assert False, "not yet supported"
for arg in args:
r1 = self.engine.dep_var_offset(arg.strip())
c1 = self.engine.r_dep_var_offset(arg.strip())
B = get_block(A, k, c1)
Bt = get_block(A, r1, k).Transpose()
Bt = Bt.Transpose()
B0 = get_block(A, r1, c1)
Md = mfem.HypreParVector(MPI.COMM_WORLD,
B0.GetGlobalNumRows(),
B0.GetColStarts())
B0.GetDiag(Md)
Bt.InvScaleRows(Md)
S = mfem.ParMult(B, Bt)
invA0 = mfem.HypreBoomerAMG(S)
invA0.iterative_mode = False
else:
cls = SparseSmootherCls[name][0]
invA0 = cls(A0, gui=self.gui[prc])
invA0.iterative_mode = False
M.SetDiagonalBlock(k, invA0)
'''
We should support Shur complement type preconditioner
if offset.Size() > 2:
B = get_block(A, 1, 0)
MinvBt = get_block(A, 0, 1)
#Md = mfem.HypreParVector(MPI.COMM_WORLD,
# A0.GetGlobalNumRows(),
# A0.GetRowStarts())
Md = mfem.Vector()
A0.GetDiag(Md)
MinvBt.InvScaleRows(Md)
S = mfem.ParMult(B, MinvBt)
invS = mfem.HypreBoomerAMG(S)
invS.iterative_mode = False
M.SetDiagonalBlock(1, invS)
'''
maxiter = int(self.maxiter)
atol = self.abstol
rtol = self.reltol
kdim = int(self.kdim)
printit = 1
sol = []
solver = mfem.GMRESSolver(MPI.COMM_WORLD)
solver.SetKDim(kdim)
#solver = mfem.MINRESSolver(MPI.COMM_WORLD)
#solver.SetOperator(A)
#solver = mfem.CGSolver(MPI.COMM_WORLD)
solver.SetOperator(A)
solver.SetAbsTol(atol)
solver.SetRelTol(rtol)
solver.SetMaxIter(maxiter)
solver.SetPreconditioner(M)
solver.SetPrintLevel(1)
# solve the problem and gather solution to head node...
# may not be the best approach
for bb in b:
rows = MPI.COMM_WORLD.allgather(np.int32(bb.Size()))
rowstarts = np.hstack((0, np.cumsum(rows)))
dprint1("rowstarts/offser", rowstarts, offset.ToList())
if x is None:
xx = mfem.BlockVector(offset)
xx.Assign(0.0)
else:
xx = x
#for j in range(cols):
# dprint1(x.GetBlock(j).Size())
# dprint1(x.GetBlock(j).GetDataArray())
#assert False, "must implement this"
solver.Mult(bb, xx)
s = []
for i in range(offset.Size() - 1):
v = xx.GetBlock(i).GetDataArray()
vv = gather_vector(v)
if myid == 0:
s.append(vv)
else:
pass
if myid == 0:
sol.append(np.hstack(s))
if myid == 0:
sol = np.transpose(np.vstack(sol))
return sol
else:
return None
# 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
# the 3D ADS preconditioners from hypre. If using hybridization, the
# system is preconditioned with hypre's BoomerAMG.
pcg = mfem.CGSolver(A.GetComm())
pcg.SetOperator(A)
pcg.SetRelTol(1e-12)
pcg.SetMaxIter(500)
pcg.SetPrintLevel(1)
if hybridization: prec = mfem.HypreBoomerAMG(A)
else:
if a.StaticCondensationIsEnabled():
prec_fespace = a.SCParFESpace()
else:
prec_fespace = fespace
if dim == 2: prec = mfem.HypreAMS(A, prec_fespace)
else: prec = mfem.HypreADS(A, prec_fespace)
pcg.SetPreconditioner(prec)
pcg.Mult(B, X)
# 13. Recover the parallel grid function corresponding to X. This is the
# local finite element solution on each processor.
a.RecoverFEMSolution(X, b, x)
# 14. Compute and print the L^2 norm of the error.
err = x.ComputeL2Error(F)
if myid == 0:
print("|| F_h - F ||_{L^2} = " + str(err))
# 15. Save the refined mesh and the solution in parallel. This output can
if (static_cond): a.EnableStaticCondensation()
a.Assemble()
A = mfem.HypreParMatrix()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B)
if verbose:
print("Size of linear system: " + str(A.GetGlobalNumRows()))
# 12. Define and apply a parallel PCG solver for AX=B with the AMS
# preconditioner from hypre.
prec_fespace = (a.SCParFESpace()
if a.StaticCondensationIsEnabled() else fespace)
ams = mfem.HypreAMS(A, prec_fespace)
pcg = mfem.HyprePCG(A)
pcg.SetTol(1e-12)
pcg.SetMaxIter(500)
pcg.SetPrintLevel(2)
pcg.SetPreconditioner(ams)
pcg.Mult(B, X)
# 13. Recover the parallel grid function corresponding to X. This is the
# local finite element solution on each processor.
a.RecoverFEMSolution(X, b, x)
# 12. Compute and print the L^2 norm of the error.
err = x.ComputeL2Error(E)
if verbose: # note that err should be evaulated on all nodes