[petsc-users] Preconditioned BiCGStab in PETSC, formulas

[Kirill Voronin]

Thank you very much for your answer!

But when I am trying to monitor convergence mfor my problem I do see 3
calls of SampleShellPCApply at each iteration step (simply printing out
something inside this function).

But looking at
http://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/impls/bcgs/bcgs.c,
I see that there should be two for each iteration of do loop.
Can this 3-d call happen due to the monitoring routines?


Actually I run code with -ksp_monitor_max -ksp_monitor_true_residual and
-ksp_monitor,
with additional monitor routine which calls KSPBuildResidual() and then
computes in NORM_1.

Best regards,

Kirill Voronin
>

> 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
>>
>>
>
>


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