[deal.II] 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

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Re: [deal.II] Facilities for computing the "goodness" of a mesh (i.e. something like a mesh-quality indicator)

[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

On 15.01.20 18:26, Krishnakumar Gopalakrishnan wrote:


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

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Re: [deal.II] Facilities for computing the "goodness" of a mesh (i.e. something like a mesh-quality indicator)

[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

On Wednesday, January 15, 2020 at 5:31:34 PM UTC, Martin Kronbichler wrote:
>
> 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
> On 15.01.20 18:26, Krishnakumar Gopalakrishnan wrote:
>
> 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
> -- 
> The deal.II project is located at http://www.dealii.org/
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>  
> 
> .
>
>

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Re: [deal.II] Facilities for computing the "goodness" of a mesh (i.e. something like a mesh-quality indicator)

[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

> On 15 Jan 2020, at 18:31, Martin Kronbichler  
> wrote:
> 
> 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
> On 15.01.20 18:26, Krishnakumar Gopalakrishnan wrote:
>> 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
>> 
>> -- 
>> The deal.II project is located at http://www.dealii.org/ 
>> 
>> For mailing list/forum options, see 
>> https://groups.google.com/d/forum/dealii?hl=en 
>> 
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>> "deal.II User Group" group.
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>> https://groups.google.com/d/msgid/dealii/3602a53a-a98a-4a5c-a512-a6d179c8dcec%40googlegroups.com
>>  
>> .
> 
> 
> -- 
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> 
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>  
> .

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Re: [deal.II] Facilities for computing the "goodness" of a mesh (i.e. something like a mesh-quality indicator)

[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.

-- 

Wolfgang Bangerth  email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

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