[petsc-users] Lowly convergenced rate of GMRES

[Barry Smith]

  Where is the matrix coming from, what discretization are you using and how large is it? Preconditioning is very dependent on the matrix in question, for example some systems arising from the Helmholtz equation are extremely difficult to precondition and often direct solvers are the best approach.

  Barry

> On Jul 23, 2017, at 9:30 PM, 李瑞 <lirui319 at hnu.edu.cn> wrote:
> 
> Dear professor or engineer:
>  I use GMRES method to solve a linear Non-Hermite equation.To improve the convergenced rate of GMRES method in limited steps,I have tried serval ways i can do.My makefile is written such following content:
> 
>>> ...
>>> -ksp_monitor -ksp_max_it 500 \ksp_type gmres \
>>> -ksp_gmres_restart 90  -ksp_atol 1.e-6 \
>>> -ksp_rtol 1.e-9  -ksp_pc_side right \
>>> -pc_type asm  -pc_asm_type restrict  -pc_asm_overlap 2 \
>>> -sub_ksp_type preonly -sub_pc_type lu 
> 
> The result is always not pleasure.
>   1 KSP Residual norm 4.436461190051e+04 
>   2 KSP Residual norm 9.773182866331e+03 
>   3 KSP Residual norm 8.432841532618e+03 
>   4 KSP Residual norm 7.642491240521e+03
>         ...... 
> 497 KSP Residual norm 5.345439499920e+02 
> 498 KSP Residual norm 5.269741944074e+02 
> 499 KSP Residual norm 5.197171806884e+02 
> 500 KSP Residual norm 5.127519507363e+02
> 
> Could you provide some ideas to increase the convergenced rate of this type of method?Thanks！
>