[petsc-users] Gmsh 8-noded quadrilateral

Fri Feb 11 15:01:52 CST 2022

Dear Matthew and Jed,

Brilliant. Thank you so much!

Your changes work like a charm Matthew (I tested your branch on the gmsh 
file I sent) and thank you so much for your advice Jed. The loss of one 
order of convergence for an inf-sup stable pressure discretization seems 
indeed a very high price to pay for the moderate increase in efficiency 
by elimination of the interior modes. You have given me food for thought 
and I will probably personally not use 8-node quadrilaterals. 
Nevertheless, for our code it will be important to support 8-node 
quadrilaterals as it is still an element widely used in solid mechanics 
simulations. LibCEED looks very interesting.

Thank you so much again.

Best wishes from Paris,
Susanne

On 11.02.2022 20:27, Matthew Knepley wrote:

> Jed is right about the numerics. However, this does not look hard. Here 
> is my try at it:
> 
> https://gitlab.com/petsc/petsc/-/merge_requests/4838
> 
> Please tell me if this works and I will make a test and merge.
> 
> Thanks,
> 
> Matt
> 
> On Thu, Feb 10, 2022 at 6:47 PM Jed Brown <jed at jedbrown.org> wrote:
> 
>> Susanne, do you want PetscFE to make the serendipity (8-node) finite 
>> element space or do you just want to read these meshes? I.e., would it 
>> be okay with you if the coordinates were placed in a Q_2 (9-node, 
>> biquadratic) finite element space?
>> 
>> This won't matter if you're traversing the dofs per edge manually, but 
>> there are some efficiency benefits of using the Q_2 space (especially 
>> if your code can use the tensor product, perhaps via a library like 
>> libCEED). Note that Q_2 spaces have better stability properties. For 
>> example, the Q_2 space is inf-sup stable with P_1 discontinuous 
>> pressure (gives third order L^2 and second order H^1 convergence), but 
>> serendipity (8-node) is only stable with piecewise constant pressure 
>> (gives second order L^2 and first order H^1 convergence).
>> 
>> Susanne Claus <susanne.claus at onera.fr> writes:
>> 
>>> Dear Matthew,
>>> 
>>> Thank you so much.
>>> I have a attached a small 8-noded quadrilateral mesh file (Version 4
>>> ASCII) generated with gmsh 4.8.4.
>>> 
>>> Best wishes,
>>> Susanne
>>> 
>>> On 10.02.2022 16:23, Matthew Knepley wrote:
>>> 
>>>> On Thu, Feb 10, 2022 at 10:12 AM Susanne Claus 
>>>> <susanne.claus at onera.fr>
>>>> wrote:
>>>> 
>>>>> Hello,
>>>>> 
>>>>> I am using DMPlex for the mesh structure of a solid mechanics 
>>>>> finite
>>>>> element code. I mainly use gmsh as input file format. When I try to
>>>>> read in 8-noded Quadrilaterals (Element type 16 in gmsh) DMPlex 
>>>>> tells
>>>>> me that this element type is unknown. However a 9-noded 
>>>>> Quadrilateral
>>>>> can be read without problem. On inspecting the plexgmsh.c source 
>>>>> code
>>>>> I can see that 8-noded quadrilaterals are deactivated:
>>>>> 
>>>>> #if 0
>>>>> 146:   {20, GMSH_TRI, 2, 3, 3,  9, NULL},
>>>>> 147:   {16, GMSH_QUA, 2, 2, 4,  8, NULL},
>>>>> 
>>>>> For our application these 8-noded quadrilateral are very important.
>>>>> 
>>>>> Is there any reason why they have not been implemented/deactivated 
>>>>> in
>>>>> the dmplex gmsh reader?
>>>> 
>>>> No, we can handle them in the same way I think. Let me look at it.
>>>> Hopefully it is easy.
>>>> 
>>>> Thanks,
>>>> 
>>>> Matt
>>>> 
>>>>> Thank you for all the great work you are doing. PETSc is amazing.
>>>>> 
>>>>> Best wishes,
>>>>> Susanne Claus
>>>> 
>>>> --
>>>> 
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which
>>>> their experiments lead.
>>>> -- Norbert Wiener
>>>> 
>>>> https://www.cse.buffalo.edu/~knepley/ [1]
>>> 
>>> --
>>> 
>>> Susanne Claus
>>> Ingénieur Chercheur
>>> Applied Mathematics and Scientific Computing Group
>>> DTIS
>>> 
>>> ONERA - The French Aerospace Lab
>>> 6 Chemin de la Vauve aux Granges, 91120 Palaiseau
>>> 
>>> Links:
>>> ------
>>> [1] http://www.cse.buffalo.edu/~knepley/
>>> $MeshFormat
>>> 4.1 0 8
>>> $EndMeshFormat
>>> $PhysicalNames
>>> 2
>>> 1 2 "Neumann"
>>> 2 1 "Domain"
>>> $EndPhysicalNames
>>> $Entities
>>> 4 4 1 0
>>> 1 0 0 0 0
>>> 2 1 0 0 0
>>> 3 1 1 0 0
>>> 4 0 1 0 0
>>> 1 -9.999999994736442e-08 -1e-07 -1e-07 1.0000001 1e-07 1e-07 0 2 1 -2
>>> 2 0.9999999000000001 -9.999999994736442e-08 -1e-07 1.0000001 
>>> 1.0000001 1e-07 1 2 2 2 -3
>>> 3 -9.999999994736442e-08 0.9999999000000001 -1e-07 1.0000001 
>>> 1.0000001 1e-07 0 2 3 -4
>>> 4 -1e-07 -9.999999994736442e-08 -1e-07 1e-07 1.0000001 1e-07 0 2 4 -1
>>> 1 -9.999999994736442e-08 -9.999999994736442e-08 -1e-07 1.0000001 
>>> 1.0000001 1e-07 1 1 4 1 2 3 4
>>> $EndEntities
>>> $Nodes
>>> 9 21 1 46
>>> 0 1 0 1
>>> 1
>>> 0 0 0
>>> 0 2 0 1
>>> 2
>>> 1 0 0
>>> 0 3 0 1
>>> 3
>>> 1 1 0
>>> 0 4 0 1
>>> 4
>>> 0 1 0
>>> 1 1 0 3
>>> 5
>>> 35
>>> 36
>>> 0.5 0 0
>>> 0.25 0 0
>>> 0.75 0 0
>>> 1 2 0 3
>>> 6
>>> 37
>>> 38
>>> 1 0.5 0
>>> 1 0.25 0
>>> 1 0.75 0
>>> 1 3 0 3
>>> 7
>>> 39
>>> 40
>>> 0.5 1 0
>>> 0.75 1 0
>>> 0.25 1 0
>>> 1 4 0 3
>>> 8
>>> 41
>>> 42
>>> 0 0.5 0
>>> 0 0.75 0
>>> 0 0.25 0
>>> 2 1 0 5
>>> 9
>>> 43
>>> 44
>>> 45
>>> 46
>>> 0.5 0.5 0
>>> 0.75 0.5 0
>>> 0.5 0.25 0
>>> 0.25 0.5 0
>>> 0.5 0.75 0
>>> $EndNodes
>>> $Elements
>>> 2 6 197 206
>>> 1 2 8 2
>>> 197 2 6 37
>>> 198 6 3 38
>>> 2 1 16 4
>>> 203 2 6 9 5 37 43 44 36
>>> 204 1 5 9 8 35 44 45 42
>>> 205 4 8 9 7 41 45 46 40
>>> 206 3 7 9 6 39 46 43 38
>>> $EndElements
> 
> --
> 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener
> 
> https://www.cse.buffalo.edu/~knepley/ [1]

-- 

Susanne Claus
Ingénieur Chercheur
Applied Mathematics and Scientific Computing Group
DTIS

ONERA - The French Aerospace Lab
6 Chemin de la Vauve aux Granges, 91120 Palaiseau

Links:
------
[1] http://www.cse.buffalo.edu/~knepley/
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