Re: [Libmesh-users] Refinement of coefficient defined on a second mesh

[Min Xu <mi...@sc...>]

The solution psi will also vary significantly nearby the source or detector 
whereas the absorption alpha may just be uniform on these places. It is hence 
beneficiary to use a more coarse mesh for alpha than that for psi.

I am now leaning toward MeshData to store alpha. I read the mailing list 
archive that MeshData did not support MeshRefinement yet. Have this situation 
changed? Is it possible to use MeshRefinement to refine the MeshData in the 
same way as the solution of an equation system is refined? How?

Thanks!

Min
On Monday 12 September 2005 21:22, John Peterson wrote:
> Min Xu writes:
>  > Hi,
>  >
>  > I am a new libmesh user. I try to solve an optimization problem for the
>  > absorption alpha, governed by the diffusion equation:
>  >       dpsi/dt = laplace(psi) - alpha*psi,
>  > such that the psi on the boundary matches the measurement. The
>  > absorption alpha is space dependent and need to be determined through
>  > optimization.
>  >
>  > The initial guess for alpha is uniform. I would like to use a coarse
>  > mesh for this parameter alpha initially and to refine this mesh
>  > gradually in the optimization process at locations where alpha changes
>  > abruptly.
>  >
>  > The solution psi will be solved on a different mesh which may start from
>  > the coefficient mesh and evolve independently.
>
> I wonder will you really need two separate meshes?  It seems that psi will
> vary a lot wherever alpha varies a lot -- they are coupled.  The one mesh
> case I think is simpler than having multiple meshes.  Then alpha is similar
> to a "lagged" coefficient which gives you a new value of psi that in turn
> feeds back in to determine the next alpha.
>
> -John