[petsc-users] Rules of choosing KSPType

[Zhenglun (Alan) Wei]

Dear All,
I hope you're having a nice day.
Compared the user manual of PETSc 3.1 and 3.4, I found that there are
several 'new' KSP types are added. Then, I have some confusions on which
KSP solver I need to pick. To my knowledge, if the matrix is symmetric,
positive definite, the CG can be used. Otherwise, I have to use GMRES.
My questions are:
1, What is the major difference among 'Conjugate Gradient', 'BiConjugate
Gradient' and 'Conjugate Gradient Squared'? As I tested, the CGS is
slightly (5%) faster than CG on solving a Poisson equation with uniform
Cartesian grid with PC = GAMG. The BiCG is not tested because it seems
not be compatible with PC = GAMG.
2, What is the major difference among GMRES, fGMRES and dGMRES.
Specially, I want to solve a Poisson equation with non-uniform Cartesian
grid. Theoretically, which 'GMRES' method would be the best for my case?

thanks,
Alan