solver for a very hetereogeneous system of equations
I am solving a FE problem on a hetereogeneous medium consisting of rigid phase (Young modulus of about 100 000 N/mm2), a softer phase (Young modulus of 20 000 N/mm2) and pore (Young modulus of 1 N/mm2). The reason that I have to mesh the pore is that there are some elements of rigid phase hanging out in the pores. So, if I do not mesh the pore, then my FE matrix is singular.
The resulting discrete system of equation is typically of 50 000 times 50 000 dimension (17 000 nodes, three dofs per node). To speed up the calculation, I have tried to use iterative solvers. To be more precise, I have used the GMRES (Generalized Minimal Residual) and AGMRES with preconditionners like incomplete LU. Unfortunately, the performance of these iteratives solvers (which to my limited knowledge, one of the best iterative solvers) is very bad. Normally, they need about 2000 iterations to get solution of precision of only 1e-05.
I solved this problem by using direct solver like SparseLU but it is just a temporary solution.
My question is that if there is any solver suitable to this very hetereogeneous system of equation?
I would much appreaciate any reply.