[petsc-users] The condition number of the ill-conditioned matrix

[w_ang_temp]

Hello,
    I have a problem about the ill-conditioned matrix. I deal with the soil-water coupled problem in
geotechnical engineering. It can be demonstrated that the stiffness matrix of soil-water coupled problem is
ill-conditioned due to the coupled effects of large relative differences in stiffnesses and permeabilities
of materials. But it should not be ill-conditioned for soil-water uncoupled problem, although there is no derivation
in papers.
    In my three models, the condition numbers are 3.5595E+05, 1.8849E+06, 9.0206E+07 for soil-water
coupled models and 5.2885E+04, 3.3826 E+05, 3.4565E+05 for soil-water uncoupled ones, respectively.
Therefore, in my opinion, the uncoupled models are also ill-conditioned due to the large condition
numbers.
    However, when using GMRES, CG and CGS, the three models of uncoupled ones show rapid convergent rate 
while coupled models have bad convergence performance.
    It is a problem in my practical project in using PETSc although it seems a weaker connections with PETSc.
So, anyone offers some clues?
    Thanks.
                                                                    Jim
 
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