[petsc-users] PCFIELDSPLIT and RHS

[tribur]

Dear PETsc team,

We are confrontated with the problem of a complex-valued equation 
system M * z = (A + i*B) * (x + i*y) = b + i*c which shows slow 
convergence using GMRES and, e.g., Block Jacobi or SOR as 
preconditioner.

To be able to use algebraic multigrid preconditioning, we are trying to 
solve the equivalent real-valued system (A -B; B A) * (x; y) = (b; c) 
using PCFIELDSPLIT and, e.g.,
-ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur 
-pc_fieldsplit_schur_fact_type full -fieldsplit_real_ksp_type gmres 
-fieldsplit_real_ksp_max_it 10 -fieldsplit_real_pc_type bjacobi 
-fieldsplit_real_sub_pc_type lu -fieldsplit_imag_ksp_type fgmres 
-fieldsplit_imag_ksp_max_it 10 -fieldsplit_imag_pc_type none

However, PCFIELDSPLIT does'nt work due to the lacking convergence of 
ksp(A) with the right hand side bTmp given by the current FGMRES 
iteration (outer loop). kspSolve(kspA, b, x) converges acceptably fast 
using, e.g., GMRES and Block Jacobi, but kspSolve(kspA, bTmp, xTmp) 
shows stagnation after about 3 iterations.

What can we do? Do think a good initial estimate for (x,y) helps?

Thanks a lot for any hints,

Kathrin