Got it. Thank you for your explanation!

Best wishes,
Zongze


On Mon, 15 May 2023 at 23:28, Matthew Knepley <knepley@gmail.com> wrote:
On Mon, May 15, 2023 at 9:55 AM Zongze Yang <yangzongze@gmail.com> wrote:
On Mon, 15 May 2023 at 17:24, Matthew Knepley <knepley@gmail.com> wrote:
On Sun, May 14, 2023 at 7:23 PM Zongze Yang <yangzongze@gmail.com> wrote:
Could you try to project the coordinates into the continuity space by enabling the option `-dm_plex_gmsh_project_petscdualspace_lagrange_continuity true`?

There is a comment in the code about that:

  /* XXX FIXME Requires DMPlexSetClosurePermutationLexicographic() */

So what is currently done is you project into the discontinuous space from the GMsh coordinates,
and then we get the continuous coordinates from those later. This is why we get the right answer.

 
Sorry, I'm having difficulty understanding the comment and fully understanding your intended meaning. Are you saying that we can only project the space to a discontinuous space? 

For higher order simplices, because we do not have the mapping to the GMsh order yet.
 
Additionally, should we always set `dm_plex_gmsh_project_petscdualspace_lagrange_continuity` to false for high-order gmsh files?

This is done automatically if you do not override it.
 
With the option set to `true`, I got the following error:

Yes, do not do that.

  Thanks,

     Matt
 
```
$ $PETSC_DIR/$PETSC_ARCH/tests/dm/impls/plex/tests/runex33_gmsh_3d_q2.sh -e "-dm_plex_gmsh_project_petscdualspace_lagrange_continuity true"
not ok dm_impls_plex_tests-ex33_gmsh_3d_q2 # Error code: 77
#       Volume: 0.46875
#       [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
#       [0]PETSC ERROR: Petsc has generated inconsistent data
#       [0]PETSC ERROR: Calculated volume 0.46875 != 1. actual volume (error 0.53125 > 1e-06 tol)
#       [0]PETSC ERROR: See https://petsc.org/release/faq/ for trouble shooting.
#       [0]PETSC ERROR: Petsc Development GIT revision: v3.19.1-294-g9cc24bc9b93  GIT Date: 2023-05-15 12:07:10 +0000
#       [0]PETSC ERROR: ../ex33 on a arch-linux-c-debug named AMA-PC-RA18 by yzz Mon May 15 21:53:43 2023
#       [0]PETSC ERROR: Configure options --CFLAGS=-I/opt/intel/oneapi/mkl/latest/include --CXXFLAGS=-I/opt/intel/oneapi/mkl/latest/include --LDFLAGS="-Wl,-rpath,/opt/intel/oneapi/mkl/latest/lib/intel64 -L/opt/intel/oneapi/mkl/latest/lib/intel64" --download-bison --download-chaco --download-cmake --download-eigen="/home/yzz/firedrake/complex-int32-mkl-X-debug/src/eigen-3.3.3.tgz " --download-fftw --download-hdf5 --download-hpddm --download-hwloc --download-libpng --download-metis --download-mmg --download-mpich --download-mumps --download-netcdf --download-p4est --download-parmmg --download-pastix --download-pnetcdf --download-ptscotch --download-scalapack --download-slepc --download-suitesparse --download-superlu_dist --download-tetgen --download-triangle --with-blaslapack-dir=/opt/intel/oneapi/mkl/latest --with-c2html=0 --with-debugging=1 --with-fortran-bindings=0 --with-mkl_cpardiso-dir=/opt/intel/oneapi/mkl/latest --with-mkl_pardiso-dir=/opt/intel/oneapi/mkl/latest --with-scalar-type=complex --with-shared-libraries=1 --with-x=1 --with-zlib PETSC_ARCH=arch-linux-c-debug
#       [0]PETSC ERROR: #1 CheckVolume() at /home/yzz/opt/petsc/src/dm/impls/plex/tests/ex33.c:246
#       [0]PETSC ERROR: #2 main() at /home/yzz/opt/petsc/src/dm/impls/plex/tests/ex33.c:261
#       [0]PETSC ERROR: PETSc Option Table entries:
#       [0]PETSC ERROR: -coord_space 0 (source: command line)
#       [0]PETSC ERROR: -dm_plex_filename /home/yzz/opt/petsc/share/petsc/datafiles/meshes/cube_q2.msh (source: command line)
#       [0]PETSC ERROR: -dm_plex_gmsh_project (source: command line)
#       [0]PETSC ERROR: -dm_plex_gmsh_project_petscdualspace_lagrange_continuity true (source: command line)
#       [0]PETSC ERROR: -tol 1e-6 (source: command line)
#       [0]PETSC ERROR: -volume 1.0 (source: command line)
#       [0]PETSC ERROR: ----------------End of Error Message -------send entire error message to petsc-maint@mcs.anl.gov----------
#       application called MPI_Abort(MPI_COMM_SELF, 77) - process 0
 ok dm_impls_plex_tests-ex33_gmsh_3d_q2 # SKIP Command failed so no diff
```


Best wishes,
Zongze

  Thanks,

     Matt
 
Best wishes,
Zongze


On Mon, 15 May 2023 at 04:24, Matthew Knepley <knepley@gmail.com> wrote:
On Sun, May 14, 2023 at 12:27 PM Zongze Yang <yangzongze@gmail.com> wrote:



On Sun, 14 May 2023 at 23:54, Matthew Knepley <knepley@gmail.com> wrote:
On Sun, May 14, 2023 at 9:21 AM Zongze Yang <yangzongze@gmail.com> wrote:
Hi, Matt,

The issue has been resolved while testing on the latest version of PETSc. It seems that the problem has been fixed in the following merge request:  https://gitlab.com/petsc/petsc/-/merge_requests/5970

No problem. Glad it is working.
 
I sincerely apologize for any inconvenience caused by my previous message. However, I would like to provide you with additional information regarding the test files. Attached to this email, you will find two Gmsh files: "square_2rd.msh" and "square_3rd.msh." These files contain high-order triangulated mesh data for the unit square.

```
$ ./ex33 -coord_space 0 -dm_plex_filename square_2rd.msh -dm_plex_gmsh_project -dm_plex_gmsh_project_petscdualspace_lagrange_continuity true -dm_plex_gmsh_project_fe_view -volume 1
PetscFE Object: P2 1 MPI process
  type: basic
  Basic Finite Element in 2 dimensions with 2 components
  PetscSpace Object: P2 1 MPI process
    type: sum
    Space in 2 variables with 2 components, size 12
    Sum space of 2 concatenated subspaces (all identical)
      PetscSpace Object: sum component (sumcomp_) 1 MPI process
        type: poly
        Space in 2 variables with 1 components, size 6
        Polynomial space of degree 2
  PetscDualSpace Object: P2 1 MPI process
    type: lagrange
    Dual space with 2 components, size 12
    Continuous Lagrange dual space
    Quadrature on a triangle of order 5 on 9 points (dim 2)
Volume: 1.
$ ./ex33 -coord_space 0 -dm_plex_filename square_3rd.msh -dm_plex_gmsh_project -dm_plex_gmsh_project_petscdualspace_lagrange_continuity true -dm_plex_gmsh_project_fe_view -volume 1
PetscFE Object: P3 1 MPI process
  type: basic
  Basic Finite Element in 2 dimensions with 2 components
  PetscSpace Object: P3 1 MPI process
    type: sum
    Space in 2 variables with 2 components, size 20
    Sum space of 2 concatenated subspaces (all identical)
      PetscSpace Object: sum component (sumcomp_) 1 MPI process
        type: poly
        Space in 2 variables with 1 components, size 10
        Polynomial space of degree 3
  PetscDualSpace Object: P3 1 MPI process
    type: lagrange
    Dual space with 2 components, size 20
    Continuous Lagrange dual space
    Quadrature on a triangle of order 7 on 16 points (dim 2)
Volume: 1.
```

Thank you for your attention and understanding. I apologize once again for my previous oversight.

Great! If you make an MR for this, you will be included on the next list of PETSc contributors. Otherwise, I can do it.


I appreciate your offer to handle the MR. Please go ahead and take care of it. Thank you!

I have created the MR with your tests. They are working for me:


  Thanks,

     Matt
 
Best Wishes,
Zongze
 
  Thanks,

     Matt
 
Best wishes,
Zongze


On Sun, 14 May 2023 at 16:44, Matthew Knepley <knepley@gmail.com> wrote:
On Sat, May 13, 2023 at 6:08 AM Zongze Yang <yangzongze@gmail.com> wrote:
Hi, Matt, 

There seem to be ongoing issues with projecting high-order coordinates from a gmsh file to other spaces. I would like to inquire whether there are any plans to resolve this problem.

Thank you for your attention to this matter.

Yes, I will look at it. The important thing is to have a good test. Here are the higher order geometry tests


I take shapes with known volume, mesh them with higher order geometry, and look at the convergence to the true volume. Could you add a GMsh test, meaning the .msh file and known volume, and I will fix it?

  Thanks,

     Matt
 

Best wishes,
Zongze


On Sat, 18 Jun 2022 at 20:31, Zongze Yang <yangzongze@gmail.com> wrote:
Thank you for your reply. May I ask for some references on the order of the dofs on PETSc's FE Space (especially high order elements)?

Thanks,

 Zongze

Matthew Knepley <knepley@gmail.com> 于2022年6月18日周六 20:02写道：
On Sat, Jun 18, 2022 at 2:16 AM Zongze Yang <yangzongze@gmail.com> wrote:
In order to check if I made mistakes in the python code, I try to use c code to show the issue on DMProjectCoordinates. The code and mesh file is attached.
If the code is correct, there must be something wrong with `DMProjectCoordinates` or `DMPlexCreateGmshFromFile` for high-order mesh.

Something is definitely wrong with high order, periodic simplices from Gmsh. We had not tested that case. I am at a conference and cannot look at it for a week.
My suspicion is that the space we make when reading in the Gmsh coordinates does not match the values (wrong order).

  Thanks,

    Matt
 
The command and the output are listed below: (Obviously the bounding box is changed.)
```
$ ./test_gmsh_load_2rd -filename cube-p2.msh -old_fe_view -new_fe_view
Old Bounding Box:
  0: lo = 0. hi = 1.
  1: lo = 0. hi = 1.
  2: lo = 0. hi = 1.
PetscFE Object: OldCoordinatesFE 1 MPI processes
  type: basic
  Basic Finite Element in 3 dimensions with 3 components
  PetscSpace Object: P2 1 MPI processes
    type: sum
    Space in 3 variables with 3 components, size 30
    Sum space of 3 concatenated subspaces (all identical)
      PetscSpace Object: sum component (sumcomp_) 1 MPI processes
        type: poly
        Space in 3 variables with 1 components, size 10
        Polynomial space of degree 2
  PetscDualSpace Object: P2 1 MPI processes
    type: lagrange
    Dual space with 3 components, size 30
    Discontinuous Lagrange dual space
    Quadrature of order 5 on 27 points (dim 3)
PetscFE Object: NewCoordinatesFE 1 MPI processes
  type: basic
  Basic Finite Element in 3 dimensions with 3 components
  PetscSpace Object: P2 1 MPI processes
    type: sum
    Space in 3 variables with 3 components, size 30
    Sum space of 3 concatenated subspaces (all identical)
      PetscSpace Object: sum component (sumcomp_) 1 MPI processes
        type: poly
        Space in 3 variables with 1 components, size 10
        Polynomial space of degree 2
  PetscDualSpace Object: P2 1 MPI processes
    type: lagrange
    Dual space with 3 components, size 30
    Continuous Lagrange dual space
    Quadrature of order 5 on 27 points (dim 3)
New Bounding Box:
  0: lo = 2.5624e-17 hi = 8.
  1: lo = -9.23372e-17 hi = 7.
  2: lo = 2.72091e-17 hi = 8.5
``` 

Thanks,
Zongze

Zongze Yang <yangzongze@gmail.com> 于2022年6月17日周五 14:54写道：
I tried the projection operation. However, it seems that the projection gives the wrong solution. After projection, the bounding box is changed! See logs below.

First, I patch the petsc4py by adding `DMProjectCoordinates`:
```
diff --git a/src/binding/petsc4py/src/PETSc/DM.pyx b/src/binding/petsc4py/src/PETSc/DM.pyx
index d8a58d183a..dbcdb280f1 100644
--- a/src/binding/petsc4py/src/PETSc/DM.pyx
+++ b/src/binding/petsc4py/src/PETSc/DM.pyx
@@ -307,6 +307,12 @@ cdef class DM(Object):
         PetscINCREF(c.obj)
         return c

+    def projectCoordinates(self, FE fe=None):
+        if fe is None:
+            CHKERR( DMProjectCoordinates(self.dm, NULL) )
+        else:
+            CHKERR( DMProjectCoordinates(self.dm, fe.fe) )
+
     def getBoundingBox(self):
         cdef PetscInt i,dim=0
         CHKERR( DMGetCoordinateDim(self.dm, &dim) )
diff --git a/src/binding/petsc4py/src/PETSc/petscdm.pxi b/src/binding/petsc4py/src/PETSc/petscdm.pxi
index 514b6fa472..c778e39884 100644
--- a/src/binding/petsc4py/src/PETSc/petscdm.pxi
+++ b/src/binding/petsc4py/src/PETSc/petscdm.pxi
@@ -90,6 +90,7 @@ cdef extern from * nogil:
     int DMGetCoordinateDim(PetscDM,PetscInt*)
     int DMSetCoordinateDim(PetscDM,PetscInt)
     int DMLocalizeCoordinates(PetscDM)
+    int DMProjectCoordinates(PetscDM, PetscFE)

     int DMCreateInterpolation(PetscDM,PetscDM,PetscMat*,PetscVec*)
     int DMCreateInjection(PetscDM,PetscDM,PetscMat*)
```

Then in python, I load a mesh and project the coordinates to P2:
```
import firedrake as fd
from firedrake.petsc import PETSc

# plex = fd.mesh._from_gmsh('test-fd-load-p2.msh')
plex = fd.mesh._from_gmsh('test-fd-load-p2-rect.msh')
print('old bbox:', plex.getBoundingBox())

dim = plex.getDimension()
#                                 (dim,  nc, isSimplex, k,          qorder, comm=None)
fe_new = PETSc.FE().createLagrange(dim, dim,      True, 2, PETSc.DETERMINE)
plex.projectCoordinates(fe_new)
fe_new.view()

print('new bbox:', plex.getBoundingBox())
```

The output is (The bounding box is changed!)
```
old bbox: ((0.0, 1.0), (0.0, 1.0), (0.0, 1.0))
PetscFE Object: P2 1 MPI processes
  type: basic
  Basic Finite Element in 3 dimensions with 3 components
  PetscSpace Object: P2 1 MPI processes
    type: sum
    Space in 3 variables with 3 components, size 30
    Sum space of 3 concatenated subspaces (all identical)
      PetscSpace Object: sum component (sumcomp_) 1 MPI processes
        type: poly
        Space in 3 variables with 1 components, size 10
        Polynomial space of degree 2
  PetscDualSpace Object: P2 1 MPI processes
    type: lagrange
    Dual space with 3 components, size 30
    Continuous Lagrange dual space
    Quadrature of order 5 on 27 points (dim 3)
new bbox: ((-6.530133708576188e-17, 36.30670832662781), (-3.899962995254311e-17, 36.2406171632539), (-8.8036464152166e-17, 36.111577025012224))
```

By the way, for the original DG coordinates, where can I find the relation of the closure and the order of the dofs for the cell?

Thanks!

  Zongze


Matthew Knepley <knepley@gmail.com> 于2022年6月17日周五 01:11写道：
On Thu, Jun 16, 2022 at 12:06 PM Zongze Yang <yangzongze@gmail.com> wrote:


在 2022年6月16日，23:22，Matthew Knepley <knepley@gmail.com> 写道：


On Thu, Jun 16, 2022 at 11:11 AM Zongze Yang <yangzongze@gmail.com> wrote:
Hi, if I load a `gmsh` file with second-order elements, the coordinates will be stored in a DG-P2 space. After obtaining the coordinates of a cell, how can I map the coordinates to vertex and edge? 

By default, they are stored as P2, not DG.

I checked the coordinates vector, and found the dogs only defined on cell other than vertex and edge, so I said they are stored as DG.
Then the function DMPlexVecGetClosure seems return the coordinates in lex order.

Some code in reading gmsh file reads that


1756:     if (isSimplex) continuity = PETSC_FALSE; /* XXX FIXME Requires DMPlexSetClosurePermutationLexicographic() */


1758:     GmshCreateFE(comm, NULL, isSimplex, continuity, nodeType, dim, coordDim, order, &fe)


The continuity is set to false for simplex.


Oh, yes. That needs to be fixed. For now, you can just project it to P2 if you want using


  Thanks,

     Matt
 
Thanks,
Zongze
You can ask for the coordinates of a vertex or an edge directly using


by giving the vertex or edge point. You can get all the coordinates on a cell, in the closure order, using

  Thanks,

     Matt
 
Below is some code load the gmsh file, I want to know the relation between `cl` and `cell_coords`.

```
import firedrake as fd
import numpy as np

# Load gmsh file (2rd)
plex = fd.mesh._from_gmsh('test-fd-load-p2-rect.msh')

cs, ce = plex.getHeightStratum(0)

cdm = plex.getCoordinateDM()
csec = dm.getCoordinateSection()
coords_gvec = dm.getCoordinates()

for i in range(cs, ce):
    cell_coords = cdm.getVecClosure(csec, coords_gvec, i)
    print(f'coordinates for cell {i} :\n{cell_coords.reshape([-1, 3])}')
    cl = dm.getTransitiveClosure(i)
    print('closure:', cl)
    break
```

Best wishes,
Zongze


--
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



--
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



--
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



--
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



--
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



--
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



--
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



--
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