When trying to solve a nonlinear heat equation system, for certain 
parameters the calculation fails with 
AztecOO::Iterate error code -4: GMRES Hessenberg ill-conditioned


while using the following code to solve:
SolverControl solver_control (dof_handler.n_dofs(),
                                  (system_rhs.l2_norm() > 0) ? 1e-8 * 
system_rhs.l2_norm() : 1e-8);
    LinearAlgebraTrilinos::SolverGMRES  solver (solver_control);

    LinearAlgebraTrilinos::MPI::PreconditionAMG preconditioner;
    LinearAlgebraTrilinos::MPI::PreconditionAMG::AdditionalData data;
    preconditioner.initialize(system_matrix, data);

    solver.solve (system_matrix, completely_distributed_update, system_rhs,
                  preconditioner);

What can I do to find and fix the problem for that error? Or should I try 
to switch to a direct solver (like UMFPACK)?
Thanks!

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