[petsc-users] Tensor product as matrix free method

[Matthew Knepley]

On Mon, Mar 31, 2014 at 11:49 AM, Mathis Friesdorf <
mathisfriesdorf at gmail.com> wrote:

> Hello everybody,
>
> for my Ph.D. in theoretical quantum mechanics, I am currently trying to
> integrate the Schroedinger equation (a linear partial differential
> equation). In my field, we are working with so called local spin chains,
> which mathematically speaking are described by tensor products of small
> vector spaces over several systems (let's say 20). The matrix corresponding
> to the differential equation is called Hamiltonian and can for typical
> systems be written as a sum over tensor products where it acts as the
> identity on most systems. It normally has the form
>
> *\sum Id \otimes Id ... Id \otimes M \otimes Id \otimes ...*
>
> where M takes different positions.I know how to explicitly construct the
> full matrix and insert it into Petsc, but for the interesting applications
> it is too large to be stored in the RAM. I would therefore like to
> implement it as a matrix free version.
> This should be possible using MatCreateMAIJ() and VecGetArray(), as the
> following very useful post points out
> http://lists.mcs.anl.gov/pipermail/petsc-users/2011-September/009992.html.
> I was wondering whether anybody already made progress with this, as I am
> still a bit lost on how to precisely proceed. These systems really are
> ubiquitous in theoretical quantum mechanics and I am sure it would be
> helpful to quite a lot of people who still shy away a bit from Petsc.
>
> Thanks already for your help and all the best, Mathis
>

1) The first thing you could try is MatShell(). However, you would have to
handle all the parallelism, which might be onerous.

2) An alternative is to explore the new TAIJ matrices. This is definitely
not for novice programmers, but it is a direct representation
    of a Kronecker product, and in addition is vectorized. Jed is the lead
there, so maybe he can comment.

  Thanks,

      Matt

-- 
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
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