CGNS supports fourth order and it's coded in PETSc, but Paraview hasn't 
implemented reading it yet. I think it would not be much work for someone 
(maybe you) to add it to Paraview. I have lots of applications on cubics, but 
not much beyond that so it hasn't risen to top priority for me.

There is an accepted extension, but the CGNS implementation is still in a 
branch.

https://cgns.github.io/ProposedExtensions/CPEX0045_HighOrder_v2.pdf
https://github.com/CGNS/CGNS/tree/CPEX45_high_order

There have been recent (announced in a blog post, yet still undocumented) 
extensions to the VTU format that would support this, but the format is so bad 
for parallel IO and time series that I haven't been motivated to extend the 
PETSc writer. Of course we would welcome contributions.

Duan Junming <junming.d...@epfl.ch> writes:

> Dear Jed,
>
>
> Thank you for your help!
>
> Now I moved the line using "DMViewFromOptions" after the function 
> "PetscDSSetObjective",
>
> and it works for "-dm_coord_petscspace_degree 3 -petscspace_degree 3".
>
>
> But when I tried degree 4:
>
> ./ex33 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -mesh_transform annulus 
> -dm_coord_space 0 -dm_coord_petscspace_degree 4 -petscspace_degree 4 
> -dm_refine 1 -dm_view cgns:test.cgns
>
> Paraview gives an empty render.
>
>
> Using degree 5:
>
> ./ex33 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -mesh_transform annulus 
> -dm_coord_space 0 -dm_coord_petscspace_degree 5 -petscspace_degree 5 
> -dm_refine 1 -dm_view cgns:test.cgns
>
> it reports:
>
>
> [0]PETSC ERROR: --------------------- Error Message 
> --------------------------------------------------------------
> [0]PETSC ERROR: No support for this operation for this object type
> [0]PETSC ERROR: Cell type quadrilateral with closure size 36
> [0]PETSC ERROR: See https://petsc.org/release/faq/ for trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.19.2, unknown
> [0]PETSC ERROR: ./ex33 on a arch-darwin-c-debug named 
> JunmingMacBook-Pro.local by Junming Mon Jun 12 20:23:04 2023
> [0]PETSC ERROR: Configure options --download-cgns --download-hdf5 
> --download-openmpi --download-triangle --with-fc=0 
> PETSC_ARCH=arch-darwin-c-debug --download-cgns
> [0]PETSC ERROR: #1 DMPlexCGNSGetPermutation_Internal() at 
> /Users/Junming/Packages/petsc/src/dm/impls/plex/cgns/plexcgns2.c:533
> [0]PETSC ERROR: #2 DMView_PlexCGNS() at 
> /Users/Junming/Packages/petsc/src/dm/impls/plex/cgns/plexcgns2.c:769
> [0]PETSC ERROR: #3 DMView_Plex() at 
> /Users/Junming/Packages/petsc/src/dm/impls/plex/plex.c:1801
> [0]PETSC ERROR: #4 DMView() at 
> /Users/Junming/Packages/petsc/src/dm/interface/dm.c:996
> [0]PETSC ERROR: #5 PetscObjectView() at 
> /Users/Junming/Packages/petsc/src/sys/objects/destroy.c:78
> [0]PETSC ERROR: #6 PetscObjectViewFromOptions() at 
> /Users/Junming/Packages/petsc/src/sys/objects/destroy.c:128
> [0]PETSC ERROR: #7 DMViewFromOptions() at 
> /Users/Junming/Packages/petsc/src/dm/interface/dm.c:940
> [0]PETSC ERROR: #8 CreateDiscretization() at ex33.c:232
> [0]PETSC ERROR: #9 main() at ex33.c:263
> [0]PETSC ERROR: PETSc Option Table entries:
> [0]PETSC ERROR: -dm_coord_petscspace_degree 5 (source: command line)
> [0]PETSC ERROR: -dm_coord_space 0 (source: command line)
> [0]PETSC ERROR: -dm_plex_box_faces 1,1 (source: command line)
> [0]PETSC ERROR: -dm_plex_simplex 0 (source: command line)
> [0]PETSC ERROR: -dm_refine 1 (source: command line)
> [0]PETSC ERROR: -dm_view cgns:test.cgns (source: command line)
> [0]PETSC ERROR: -mesh_transform annulus (source: command line)
> [0]PETSC ERROR: -petscspace_degree 5 (source: command line)
> [0]PETSC ERROR: ----------------End of Error Message -------send entire error 
> message to petsc-ma...@mcs.anl.gov----------
> --------------------------------------------------------------------------
> MPI_ABORT was invoked on rank 0 in communicator MPI_COMM_SELF
> with errorcode 56.
>
>
> Does cgns work for degree >= 4?
>
>
> Junming
>
>
> ________________________________
> From: Jed Brown <j...@jedbrown.org>
> Sent: Monday, June 12, 2023 19:07
> To: Duan Junming; Matthew Knepley
> Cc: petsc-users@mcs.anl.gov
> Subject: Re: [petsc-users] dm_view of high-order geometry/solution
>
> And here's an MR to do what you want without any code/arg changes.
>
> https://gitlab.com/petsc/petsc/-/merge_requests/6588
>
> Jed Brown <j...@jedbrown.org> writes:
>
>> Duan Junming <junming.d...@epfl.ch> writes:
>>
>>> Dear Jed,
>>>
>>>
>>> Thank you for the suggestion.
>>>
>>> When I run tests/ex33.c with
>>>
>>> ./ex33 -dm_plex_simplex 0 -dm_plex_box_faces 1,1 -mesh_transform annulus 
>>> -dm_coord_space 0 -dm_coord_petscspace_degree 3 -dm_refine 1 -dm_view 
>>> cgns:test.cgns
>>>
>>> and load it using Paraview,
>>>
>>> the mesh is still with straight lines.
>>
>> Ah, the viewer is keyed on the field (since the CGNS as supported by 
>> Paraview specifies coordinates and fields in the same space). That doesn't 
>> exist in your case. If you apply this patch and add `-petscspace_degre 3` to 
>> your command, you'll see that high order information is present. Paraview 
>> doesn't render as curves in all views, but it has the data.
>>
>> diff --git i/src/dm/impls/plex/tests/ex33.c w/src/dm/impls/plex/tests/ex33.c
>> index 803095bc082..590facfa4f4 100644
>> --- i/src/dm/impls/plex/tests/ex33.c
>> +++ w/src/dm/impls/plex/tests/ex33.c
>> @@ -198,7 +198,6 @@ PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *ctx, DM 
>> *dm)
>>    default:
>>      SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Unknown mesh transform %d", 
>> ctx->meshTransform);
>>    }
>> -  PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
>>    PetscFunctionReturn(PETSC_SUCCESS);
>>  }
>>
>> @@ -227,6 +226,7 @@ static PetscErrorCode CreateDiscretization(DM dm, AppCtx 
>> *ctx)
>>    PetscCall(DMCreateDS(dm));
>>    PetscCall(DMGetDS(dm, &ds));
>>    PetscCall(PetscDSSetObjective(ds, 0, volume));
>> +  PetscCall(DMViewFromOptions(dm, NULL, "-dm_view"));
>>    PetscFunctionReturn(PETSC_SUCCESS);
>>  }
>>
>>
>> I can update the viewer to handle the degenerate case of no field (all my 
>> models have fields).

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