[Nek5000-users] Building mass and stiffness matrices

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

Hi Davide,

Yes - this is also possible.  In fact, it is really quite easy --
nek is very good at computing weighted inner products.

Paul


On Tue, 18 Feb 2014, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Paul,
> It is possible to perform the online phase of rom approach in nek5000?
> After the computation of pod basis, for example,
> The reduced stiffness matrix will be of form Z^T A Z,  Where A is the
> stiffness matrix of full discretization and parameter ind., Z is the matrix
> obtain columnwise by pod basis. That implies to do not  extract
> the stiffness matrix, but to perform a new directed computation of reduced
> system inside nek5000 and select the parameter by datafile to obtain the
> online snapshot.
> In this case the reduced stiffness matrix will be , of course dense, but
> cheaper. However , it is needed to work around in order to have ah matrix
> component  and perform pointwise the tensor product z^t a z ( maybe with
> routine mxm). Maybe with new rb-hybrid approch it is possible to extend on
> the A constructed by block refering each one to a physical domain.
> Best regard
> Davide
>
>
> Il martedì 18 febbraio 2014, <nek5000-users at lists.mcs.anl.gov> ha scritto:
>
>>
>> Hi Giuseppe,
>>
>> It occurs to me that the right way to address your
>> problem is to dump out the unassembled matrices, which
>> are all block diagonal, with full blocks.  Then, in addition,
>> it's easy to write out the matrix that assembles the submatrices
>> into the full sparse matrix.  That part should be relatively
>> easy to handle in a framework that is designed to work with
>> the global index set.  (Nek doesn't deal with the global
>> indices and for the size matrix you want, in parallel, it
>> wouldn't be easy to generate them.)
>>
>> So, basically, Nek would produce
>>
>>     A_L = block_diag {A^e} _{e=1}^E
>>
>> and Boolean assembly matrix Q such that
>>
>>     A = Q^T A_L Q
>>
>> The elemental matrices, A^e, are completely full. Thus, for
>> N=9, corresponding to 10 x 10 x 10 = 1000 points in a given
>> element, you would have 1 million nonzeros in each matrix.
>> (For undeformed geometries, some of the matrices are sparser.)
>> The matrix Q^T is rectangular and consists of columns of the
>> identity matrix.  (See, e.g., Deville, F., & Mund, 2002).
>> It probably wouldn't take much effort to code up the output
>> routines for this plus some matlab code to demo how to
>> assemble the stiffness matrix.
>>
>> 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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>
>
> -- 
> Davide Baroli, PhD student
> MOX - Modeling and Scientific Computing
> Mathematics Dept.
> Politecnico di Milano
> Via Bonardi 9, 20133 Milano, Italy
>