[petsc-users] Tensor product as matrix free method

[Dominic Meiser]

Have you considered using a matrix shell:

http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreateShell.html

What operations do you need to support besides sparse matrix vector 
products?

On 03/31/2014 10:49 AM, Mathis Friesdorf 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


-- 
Dominic Meiser
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