darcyOp.SetBlock(0, 1, BT)
darcyOp.SetBlock(1, 0, B)
MinvBt = mfem.Transpose(B)
Md = mfem.Vector(M.Height())
M.GetDiag(Md)
for i in range(Md.Size()):
MinvBt.ScaleRow(i, 1 / Md[i])
S = mfem.Mult(B, MinvBt)
invM = mfem.DSmoother(M)
invS = mfem.GSSmoother(S)
invM.iterative_mode = False
invS.iterative_mode = False
darcyPrec = mfem.BlockDiagonalPreconditioner(block_offsets)
darcyPrec.SetDiagonalBlock(0, invM)
darcyPrec.SetDiagonalBlock(1, invS)
maxIter = 500
rtol = 1e-6
atol = 1e-10
stime = clock()
solver = mfem.MINRESSolver()
solver.SetAbsTol(atol)
solver.SetRelTol(rtol)
solver.SetMaxIter(maxIter)
solver.SetOperator(darcyOp)
solver.SetPreconditioner(darcyPrec)
solver.SetPrintLevel(1)
S0inv.SetOperator(matS0)
S0inv.SetPrintLevel(-1)
S0inv.SetRelTol(prec_rtol)
S0inv.SetMaxIter(prec_maxit)
Shatinv = mfem.CGSolver()
Shatinv.SetOperator(Shat)
Shatinv.SetPrintLevel(-1)
Shatinv.SetRelTol(prec_rtol)
Shatinv.SetMaxIter(prec_maxit)
# Disable 'iterative_mode' when using CGSolver (or any IterativeSolver) as
# a preconditioner:
S0inv.iterative_mode = False
Shatinv.iterative_mode = False
P = mfem.BlockDiagonalPreconditioner(offsets)
P.SetDiagonalBlock(0, S0inv)
P.SetDiagonalBlock(1, Shatinv)
# 10. 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.
mfem.PCG(A, P, b, x, 1, 200, 1e-12, 0.0)
LSres = mfem.Vector(s_test)
B.Mult(x, LSres)
LSres -= F
res = sqrt(matSinv.InnerProduct(LSres, LSres))
print("|| B0*x0 + Bhat*xhat - F ||_{S^-1} = " + str(res))