[petsc-users] Multiple phi-function evaluations (SLEPc)

[Jose E. Roman]

In a basic Arnoldi implementation, it would be possible to do what you suggest: run Arnoldi once and compute the three approximations from it. But SLEPc's implementation is a restarted method, where the computed Krylov basis is discarded when the maximum dimension is reached. Not sure how this would interact with what you propose. I think it would be feasible, but there could be issues such as each phi_k function converging at different rates. Also, the user interface for this functionality would not fit well with the current interface.

I am interested in getting feedback from you related to the performance of the MFN solver with your problem, i.e., convergence and timings. If you want, contact me to my personal email and we can discuss further and see if the multiple phi-function stuff can be accomodated in the current solver.

Jose


> El 27 ene 2022, a las 17:21, Pierre Seize <pierre.seize at onera.fr> escribió:
> 
> Hello PETSc and SLEPc users
> 
> I read that I can ask questions regarding SLEPc here, so here I go:
> 
> I'm using SLEPc to compute some phi-functions of a given matrix A. At some point I want to compute phi_0(A)b, phi_1(A)b and phi_1(hA)b where h is a scalar coefficient and b a given vector.
> 
> If I'm correct, I could reuse some information, as the Krylov decomposition used in those three computation is the same. Only the matrix used in the Pade approximant changes with the scalar coefficient, and phi function with different indices can be evaluated together. What's the most efficient way to get the three desired results with SLEPc ?
> 
> 
> As always, thank you for your help, other users and the PETSc / SLEPc teams.
> 
> 
> Pierre Seize
>