[petsc-users] Preconditioned BiCGStab in PETSC, formulas

[Barry Smith]

   The source code can be found at src/ksp/ksp/impls/bcgs/bcgs.c or nicely formatted at http://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/impls/bcgs/bcgs.c.html#KSPBCGS   You can easily find it by typing KSPBCGS into google clicking on the first link and then clicking on where it says Location:

    There are two KSP_PCApplyBAorAB() apply within the do loop. Depending on left or right preconditioning (it supports both) there is an additional apply before or after the do loop.

  Barry


> On Jan 25, 2015, at 11:02 PM, Kirill Voronin <kvoronin at labchem.sscc.ru> wrote:
> 
> 
> Hello!
> 
> I'm solving the system with user-defined preconditioned BiCGStab from PETSc.
> 
> The question is - how exactly preconditioned BiCGStab looks like (as an
> algorithm) in PETSC?
> It can be right or left or some other type of preconditioning.
> 
> The output of my code shows that during each iteration PCApply (matvec of
> preconditioner) is called 3 times and looking at Saad's version of
> nonpreconditioned BiCGStab algorithm it is not that obvious for me where
> these 3 calls exactly occur.
> 
> Saad's version:
> 
> 1.Compute r0 = b - Ax0, r0* - arbitrary.
> 2.p0 := r0
> 3.for j = 0, 1 ... till convergence, do
> 4.  alpha_j := (r_j, r0*) / (Ap_j, r0*)
> 5.  s_j := r_j - alpha_j Ap_j
> 6.  omega_j = (As_j, s_j) / (As_j, As_j)
> 7.  x_{j+1} := x_j + alpha_j p_j + omega_j s_j
> 8.  r_{j+1} := s_j - omega_j As_j
> 9.  beta_j := (r_{j+1}, r0*)/(r_j, r0*)  * alpha_j/omega_j
> 10. p_{j+1} := r_{j+1} + beta_j (p_j - omega_j Ap_j)
> 11. end do
> 
> (from Saad Y. "Iterative methods for sparce linear systems")
> 
> Thank you in advance!
> 
> -- 
> 
> Best regards,
> 
> Kirill Voronin
>