[Nek5000-users] over-integration

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

Hi Praveen, Josh,

Overintegration and dealiasing are the same.  (Aliasing corresponds
to subsampling in the integrand --- overintegration properly samples.)

Also, note that to get back to the coarse grid we actually use the
transpose of the interpolation operator --- this corresponds to
"sampling the test function on the fine grid" ...

It is possible to use over integration on any function --- one needs
to think about whether it's on the right-hand side or in some implicit
substep.

Also, we have a forthcoming paper on the topic...

Paul


On Thu, 24 Jan 2013, nek5000-users at lists.mcs.anl.gov wrote:

> The developers can correct me if I'm wrong here, but nek doesn't actually
> use over-integration, although it does something similar (dealiasing).  If
> we are computing, for example, u * u (u is vx in nek), the steps are :
>
> 1) Interpolate u to the higher space (given by lxd, lyd, lzd) (Nek has
> arrays for this already...for velocity, they are vxd, vyd, vzd)
> 2) Compute the product ud*ud on the higher order grid
> 3) Interpolate the solution back to the original space (lx1,ly1,lz1)
>
> I'm not aware of a mass matrix on the "dealiasing" mesh.
>
> Josh
>
>
> On Thu, Jan 24, 2013 at 3:13 AM, <nek5000-users at lists.mcs.anl.gov> wrote:
>
>> Hello
>> nek5000 can use over-integration for the quadratic nonlinear terms by
>> setting lxd, lyd, lzd. Is it possible to use this for integration to
>> approximate some integral like applying Biot-Savart law ? I have seen the
>> use of the mass matrices bm1 and bm2 on the velocity and pressure meshes.
>> Is there a mass matrix on the mesh (lxd,lyd,lzd) also which can be used for
>> integration ?
>>
>> I have read about the use of over-integration as a stabilization method.
>> Can you suggest some papers/books which discuss the theory behind this ?
>>
>> Thanks
>> praveen
>>
>> _______________________________________________
>> Nek5000-users mailing list
>> Nek5000-users at lists.mcs.anl.gov
>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>
>>
>
>
> -- 
> Josh Camp
>
> "All that is necessary for the triumph of evil is that good men do nothing"
> -- Edmund Burke
>