[Nek5000-users] Building mass and stiffness matrices

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

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
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