On Wed, 25 Jul 2018 at 12:24, Buesing, Henrik < hbues...@eonerc.rwth-aachen.de> wrote:
> The problem is from two-phase flow in porous media. I have written down > the equations and the operators from the 2x2 block Jacobian (see > attachment). > Have you just tried plain old multiplicative firldplit with LU as the preconditioned for the diagonal blocks? What are the iteration counts like? I think that choice should not be terrible for this system. I'd try this first before looking at Schur complements. The J11 block of the Jacobian is made elliptic. > > > > Maybe someone could tell me how to go on from there to build a good > preconditioner? > > Thank you! > Henrik > > > > > > -- > > Dipl.-Math. Henrik Büsing > > Institute for Applied Geophysics and Geothermal Energy > > E.ON Energy Research Center > > RWTH Aachen University > > > > Mathieustr. 10 | Tel +49 (0)241 80 49907 > > 52074 Aachen, Germany | Fax +49 (0)241 80 49889 > > > > http://www.eonerc.rwth-aachen.de/GGE > > hbues...@eonerc.rwth-aachen.de > > > > *Von:* Dave May <dave.mayhe...@gmail.com> > *Gesendet:* Mittwoch, 25. Juli 2018 11:37 > *An:* Buesing, Henrik <hbues...@eonerc.rwth-aachen.de> > *Cc:* Matthew Knepley <knep...@gmail.com>; PETSc <petsc-users@mcs.anl.gov> > > > *Betreff:* Re: [petsc-users] Fieldsplit - Schur Complement Reduction - > Efficient Preconditioner for Schur Complement > > > > > > > > On 25 July 2018 at 10:34, Buesing, Henrik <hbues...@eonerc.rwth-aachen.de> > wrote: > > Dear Matt! Dear Dave! > > > > Thank you for your messages! I pursued your option 1) and the solver I > sent is what I ended up with. Thus, I would like to pursue option 2): Find > a better preconditioner than the a11 block. > > > From a technical viewpoint I understand how I would build a matrix that is > used as a preconditioner for the Schur complement. > But, from a mathematical viewpoint I do not know what to assemble. How do > I find a good preconditioner for my problem? How would I tackle such a > problem? > > > > Where does your discrete saddle point system come from? > > Stokes? Navier Stokes? Something else? > > Maybe someone on the list can advise you. > > > > > Thank you! > Henrik > > > > > > -- > > Dipl.-Math. Henrik Büsing > > Institute for Applied Geophysics and Geothermal Energy > > E.ON Energy Research Center > > RWTH Aachen University > > > > Mathieustr. 10 > <https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g> | > Tel +49 (0)241 80 49907 > > 52074 Aachen, Germany | Fax +49 (0)241 80 49889 > > > > http://www.eonerc.rwth-aachen.de/GGE > > hbues...@eonerc.rwth-aachen.de > > > > *Von:* Dave May <dave.mayhe...@gmail.com> > *Gesendet:* Mittwoch, 25. Juli 2018 11:14 > *An:* Matthew Knepley <knep...@gmail.com> > *Cc:* Buesing, Henrik <hbues...@eonerc.rwth-aachen.de>; PETSc < > petsc-users@mcs.anl.gov> > *Betreff:* Re: [petsc-users] Fieldsplit - Schur Complement Reduction - > Efficient Preconditioner for Schur Complement > > > > > > > > On 25 July 2018 at 09:48, Matthew Knepley <knep...@gmail.com> wrote: > > On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik < > hbues...@eonerc.rwth-aachen.de> wrote: > > Dear all, > > I would like to improve the iterative solver [1]. As I understand it I > would need to improve the preconditioner for the Schur complement. > > How would I do that? > > > > 1) I always start from the exact thing (full Schur factorization with > exact solves and back off parts until I am happy) > > > > 2) Is the a11 block a good preconditioner for your Schur complement? If > not, I would start by replacing that matrix > > with something better. > > > > Some additional info. If you want to pursue option 2, you need to do call > > > > PCFieldSplitSetSchurPre() > > > > > http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurPre.html#PCFieldSplitSetSchurPre > > > > with PC_FIELDSPLIT_SCHUR_PRE_USER > <http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSchurPreType.html#PCFieldSplitSchurPreType> > (second arg) and your user defined schur complement preconditioner (last > arg). > > > > Thanks, > > Dave > > > > > > Thanks, > > > > Matt > > > > Thank you for your help! > Henrik > > > > [1] > -ksp_max_it 100 -ksp_rtol 1e-6 -ksp_atol 1e-50 -ksp_type fgmres -pc_type > fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition a11 > -fieldsplit_p_w_ksp_type preonly -fieldsplit_S_n_ksp_type gmres > -fieldsplit_p_w_pc_type hypre -fieldsplit_p_w_pc_hypre_type boomeramg > -fieldsplit_S_n_pc_type hypre -fieldsplit_S_n_pc_hypre_type boomeramg > -fieldsplit_S_n_ksp_max_it 100 fieldsplit_S_n_ksp_rtol 1e-2 > > > -- > Dipl.-Math. Henrik Büsing > Institute for Applied Geophysics and Geothermal Energy > E.ON Energy Research Center > RWTH Aachen University > > Mathieustr. 10 > <https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g> | > Tel +49 (0)241 80 49907 > 52074 Aachen, Germany | Fax +49 (0)241 80 49889 > > http://www.eonerc.rwth-aachen.de/GGE > hbues...@eonerc.rwth-aachen.de > > > > > -- > > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener > > > > https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/> > > > > >
