Choices of preconditioners and linear solver options in SNES and NEWTON solver for instabilities

Question

Hi All,

I have been solving phase field fracture problems using FEnics and the code converges when there is a single instability occurring but i run into convergence problems when multiple instabilities occur simultaneously. My solver options are for phase field scalar variable is

snes_solver_parameters_bounds = {"nonlinear_solver": "snes",
#                          "reset_jacobian":True,
                          "symmetric": True,
                          "snes_solver": {"maximum_iterations": 500,
                                          "linear_solver": "cg",
                                          "preconditioner": "hypre_amg",
                                          "report": False,
                                          "line_search": "basic",
                                          "method":"vinewtonrsls",
                                          "absolute_tolerance":1e-5,
                                          "relative_tolerance":1e-5,
                                          "krylov_solver": {"absolute_tolerance":1e-5,
                                                            "relative_tolerance":1e-5},
                                          "lu_solver": {"reuse_factorization": False}}}

and for the displacement is

prm['newton_solver']['linear_solver'] = 'cg'
prm['newton_solver']['preconditioner'] = 'hypre_amg'
prm['newton_solver']['absolute_tolerance'] = 1E-3
prm['newton_solver']['relative_tolerance'] = 1E-3
prm['newton_solver']['maximum_iterations'] = 500
prm['newton_solver']['relaxation_parameter'] = 1.0

What is a good choice of solver options in such a scenario? Are there other preconditioners that I could try? I understand that this is a very general question, although I have been trying different solver options but I haven't been able to figure out what the best choice is. I would appreciate any help in this regard.