Facilities for computing the "goodness" of a mesh (i.e. something like a mesh-quality indicator)

[Krishnakumar Gopalakrishnan]

In the results/extension section of Step-6 as well in Step-49, there is a great deal of discussion about obtaining good meshes are for a problem, with the caveat that this is a highly specialized topic. Step-49 is full of warnings about things that can go wrong when applying certain transformations, and it seems to implant doubts in my mind that my meshes are never going to be correct :)

Given this, in the spirit of the Kelly Indicator for solution errors in a cell, is there a similar single-metric for the quality/goodness of each cell in a mesh? Maybe there is something based on the smallest internal angle (to prevent slivers, for Jacobian of the mapping to be invertible, to prevent inverted cells etc).

After all, error estimation is a complicated topic. nevertheless the Kelly Indicator seems to do a reasonable job for quite a few equations. If currently not implemented in Deal.II, is there any journal article that discusses research in this direction?

Krishna

[Martin Kronbichler]

Dear Krishna,

We have recently added one such function, namely GridTools::compute_aspect_ratio_of_cells(),

https://dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a2a9d8801d952ea8afa9ec1573229a329

Best,
Martin

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[Krishnakumar Gopalakrishnan]

Hi Martin,

Thank you. This is certainly looking useful.  Do we have any example usage of this function? For example, how do we re-compute the mesh based on the return value from this aspect_ratio function or something?

Krishna

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[Jean-Paul Pelteret]

Dear Krishna,

There is also this long-standing pull request

https://github.com/dealii/dealii/pull/8196

that hooks into the Verdict library to do mesh quality assessment. One day, hopefully in the not too distant future, I’ll get back to integrating it into the deal.II library. But you could always extract the salient portions of that code for your purposes.

Best,

Jean-Paul

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[Wolfgang Bangerth]

On 1/15/20 10:42 AM, Krishnakumar Gopalakrishnan wrote:
>
> Thank you. This is certainly looking useful.  Do we have any example usage of
> this function? For example, how do we re-compute the mesh based on the return
> value from this aspect_ratio function or something?

Other than the functions Jean-Paul referred to, and the
GridTools::laplace_transform() function, there is nothing in deal.II for this
purpose.

But I took the liberty to write a few statements in the discussion in step-6
on this topic:
https://github.com/dealii/dealii/pull/9344

Best
W.

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Wolfgang Bangerth email: bang...@colostate.edu
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