[petsc-users] Gmsh 8-noded quadrilateral

Fri Feb 11 15:59:48 CST 2022

Sounds good. Note that if you use direct solvers, that extra node is basically free because the vertex separators are unchanged. It's a marginal cost in the storage of assembled matrices and the length of state vectors. And in 3D, even less significant.

Susanne Claus <susanne.claus at onera.fr> writes:

> 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/