Hello Miguel,
Refine by error_frac or elem_frac in libMesh (elem_frac
works better in my experience) will refine the top x*100 % of the elements
as indicated by the error vector. So if you set elem_frac = 0.1, libMesh
will refine 10 % of the current elements, starting from the element with
the highest error. If you refine with elem_frac = 0.1, libMesh will refine
all elements which have error within 10% of the highest error.
Thanks.
On Thu, Feb 16, 2017 at 12:37 PM, Salazar De Troya, Miguel <
[email protected]> wrote:
> I thought that a Dorfler strategy would be more favorable to situations
> with a singularity, where the error in certain regions is more dominant. If
> we refine a fraction of the elements, we would keep refining elements with
> errors that are not as large as the ones in the singularity, whereas with
> Dorfler, more effort is concentrated in the singularity.
>
>
>
> Miguel
>
>
>
> *From: *<[email protected]> on behalf of Vikram Garg <
> [email protected]>
> *Date: *Tuesday, February 14, 2017 at 11:26 AM
> *To: *"Paul T. Bauman" <[email protected]>
> *Cc: *"Salazar De Troya, Miguel" <[email protected]>, "
> [email protected]" <[email protected]>
> *Subject: *Re: [Libmesh-users] Criteria for marking strategy
>
>
>
> Hello Salazar,
>
> I would think that the importance of using an
> optimal marking strategy such as Dorfler depends on how difficult you think
> it will be to see gains with AMR. For example, if your underlying solution
> does not have singularities or boundary layers, it becomes more important
> to try and equalize errors across elements, make the most of each new dof
> added and so on.
>
>
>
> However, if the underlying solution does have such sharp features, I would
> not expect to see many gains over using an optimal marking strategy over a
> more heuristic one like refine_frac or the others which libMesh currently
> supports. In such problems, the solution can effectively be seen as a sum
> of a singular and non-singular component, and it is the equalization of
> error in these two components that we seek first. And AMR should be able to
> do this without pretty well needing sophisiticated marking strategies.
>
>
>
> The interesting question whether this holds for goal oriented refinement
> as well. Note that for non-singular/boundary-layer problems/adjoint
> systems, we expect the QoI to converge at twice the rate of the global H1
> solution, with the usual Galerkin (non-stabilized) formulations. Here
> again, goal-oriented AMR will only offer an improvement in the convergence
> constant, but for an error that is already decreasing fast, and I would
> again expect Dorfler type marking strategies to become more important. But
> for problems where the forward or adjoint problem has singular behaviour,
> we have seen tremendous benefits from AMR using the marking strategies
> already present in libMesh.
>
>
>
> I am admittedly not well versed with the optimal marking strategies, so if
> anyone can pick holes in these arguments, please do so.
>
>
>
> Thanks.
>
>
>
> On Tue, Feb 14, 2017 at 11:35 AM, Paul T. Bauman <[email protected]>
> wrote:
>
> On Mon, Feb 13, 2017 at 6:03 PM, Salazar De Troya, Miguel <
> [email protected]> wrote:
>
> >
> > I’ve read in several papers that in AMR the most common marking strategy
> > is Dorfler marking, which is mathematically grounded.
>
>
> There is some theory that, under some other regularity assumptions (that
> can be proven for quite a few problems), Dorfler marking provides
> optimality for the adaptive refinement process. I admit I'm not deeply
> familiar with the theory. Carsetensen's paper (
> https://arxiv.org/pdf/1312.1171.pdf) and Nochetto's review paper (
> http://www-users.math.umd.edu/~rhn/lectures/adaptivity.pdf) are probably
> good starting points (both have been on my "to read" list for awhile now).
>
>
> > However, I have not seen this implemented in libMesh.
>
>
> It looks as though it's not. Patches welcome! (I would envision this would
> be dropped in MeshRefinement as flag_elements_by_dorfler() or some such.)
>
>
> > I believe that this marking strategy does not consider the coarsening
> > portion of the refinement.
>
>
> I believe there might be some extensions through brief Googling, but I
> haven't read anything in detail. Nevertheless, it is noted that coarsening
> is really only important for unsteady problems as, theoretically, optimal
> adaptive refinement for steady problems does not require coarsening.
>
>
> > On which theories are the current marking strategies libMesh implements
> > based?
> >
>
> Maximum strategies, i.e. refine some fraction of the max (which goes back
> to Babuska).
>
> Best,
>
> Paul
>
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>
>
>
>
> --
>
> Vikram Garg
>
> Postdoctoral Associate
>
> The University of Texas at Austin
>
>
>
> http://vikramvgarg.wordpress.com/
>
> http://www.runforindia.org/runners/vikramg
>
--
Vikram Garg
Postdoctoral Associate
The University of Texas at Austin
http://vikramvgarg.wordpress.com/
http://www.runforindia.org/runners/vikramg
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