[Nek5000-users] Building mass and stiffness matrices

[nek5000-users at lists.mcs.anl.gov]

Hi Giuseppe,

Just so you're aware, 3000 elements with lx1=10 in 3D
would entail 3 billion nonzeros for the stiffness and
convective matrices, each, so 24 GB files for each matrix
(actually, 48 GB, because you need the CSR pointers).

Presumably you would need to do something clever about
parallel i/o.

How many processors are you using?

Paul




On Thu, 13 Feb 2014, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Paul,
> thank you for your answer, now I understand why I couldn't find the matrices in the code.
> For the mass matrix I think it is clear how to proceed, but how could I do the same for the stiffness matrix and the convective matrix?
> My problem consists in about 3000 elements, with lx1=10, but I plan to move to 6000 or 9000 elements.
> I will now work on a subroutine for this task, then I will come back if I find other issues.
> Giuseppe
>
>
>
>
> Il giorno 13/feb/2014, alle ore 13:34, <nek5000-users at lists.mcs.anl.gov>
> <nek5000-users at lists.mcs.anl.gov> ha scritto:
>
>>
>> Hi Giuseppe,
>>
>> Nek uses a completely matrix-free approach.  The standard way to generate
>> a matrix in this case is to start passing in unit column vectors, e_j
>> (the jth column of the Identity matrix) and saving the result a_j, the
>> jth column of A.   For sparse matrices there is a fair amount of bookeeping required so that you store only the nonzeros.  (I normally
>> use compressed sparse row format to do so.)
>>
>> The mass matrix is diagonal and therefore readily retrieved.
>>
>> How large is your problem (i.e., how many elements and what is the
>> order, lxl) ?
>>
>> Note that the number of nonzeros scales like E*(lx1^6).
>>
>> Paul
>>
>> On Thu, 13 Feb 2014, nek5000-users at lists.mcs.anl.gov wrote:
>>
>>> Dear users and developers,
>>> I am using NEK5000 for a 3d unsteady simulation with mixed Dirichlet and
>>> periodic bc. For the post-processing (a POD-based dynamics) I need the global
>>> mass and stiffness matrices as built by NEK5000 on my mesh. I would also need
>>> the matrix having as entries (phi_i, grad(phi_j)) where phi are the basis
>>> polynomials.  Is it possible to have NEK build these matrices and then save
>>> them on file? The ultimate goal is to import them on a PETSc program to
>>> perform some algebraic manipulations. I already found a way to import the
>>> simulations' results.  Surfing the code, I have found some 1-d routines, but
>>> I don't know how to extend them to my needs.  Thank you in advance for any
>>> help or hint.
>>> Best regards,
>>> Giuseppe
>>>
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