[petsc-dev] PETSc LU, Lapack and Preconditioning Matrices

[Dave Nystrom]

Matthew Knepley writes:
 > On Fri, Dec 16, 2011 at 9:37 AM, Dave Nystrom <dnystrom1 at comcast.net> wrote:
 > 
 > > I'm trying to figure out whether I can do a couple of things with petsc.
 > >
 > > 1.  It looks like the preconditioning matrix can actually be different from
 > > the full problem matrix.  So I'm wondering if I could provide a different
 > > preconditioning matrix for my problem and then do an LU solve of the
 > > preconditioning matrix using the -pc_type lu as my preconditioner.
 > 
 > Yes, that is what it is for.

Thanks.  I think I will try that and see what sort of results I get.  This
sounds like a very encouraging discovery to me.

 > > 2.  When I build petsc, I use the --download-f-blas-lapack=yes option.  I'm
 > > wondering if petsc uses lapack under the hood or has the capability to use
 > > lapack under the hood when one uses the -pc_type lu option.  In particular,
 > > since my matrices are band matrices from doing a discretization on a 2d
 > > regular mesh, I'm wondering if the petsc lu solve has the ability to use
 > > the lapack band solver dgbsv or dgbsvx.  Or is it possible to use the
 > > lapack band solver through one of the external packages that petsc can
 > > interface with.  I'm interested in this capability for smaller problem
 > > sizes that fit on a single node and that make sense.
 > 
 > We do not have any banded matrix stuff. Its either dense or sparse right
 > now.

OK.  I had always been used to thinking of a banded system as sparse,
relatively speaking, when compared to a full system.  Based also on Barry's
response, I guess I am not well enough educated on the nuances of sparse
versus banded.  For instance, when I use "-ksp_type preonly -pc_type lu" to
solve one of my systems, I had assumed that the LU factorization computed by
petsc was really filling in the 2*nx+1 bandwidth even though petsc might not
be explicitly using the banded nature of the matrix.  So I am not sure at all
what is going on under the hood in petsc for this set of solver options.  Nor
do I really know how to find out without reading the source code which might
be fairly daunting.

 > > 3.  I'm also wondering how I might be able to learn more about the petsc
 > > ilu capability.  My impression is that it does ilu(k) and I have tried
 > > it with k>0 but am wondering if one of the options might allow it to do
 > > ilut and whether as k gets big whether ilu(k) approximates lu.  I
 > > currently do not understand the petsc ilu well enough to know how much
 > > extra fill I get as I increase k and where that extra fill might be
 > > located for the case of a band matrix that one gets from discretization
 > > on a regular 2d mesh.
 > 
 > We do not do ilu(dt). Its complicated, and we determined that it was not
 > worth the effort. You can get that from Hypre is you want. Certainly, for
 > big enough k, ilu(k) is lu but its a slow way to do it.

Thanks.  I need to experiment more with ilu(k) on a couple of my linear
systems.

 > Matt
 > 
 > 
 > > Thanks,
 > >
 > > Dave