[petsc-users] examples of DMPlex*FVM methods

[Jed Brown]

Ingo Gaertner <ingogaertner.tus at gmail.com> writes:

> We have never talked about Riemann solvers in our CFD course, and I don't
> understand what's going on in ex11.
> However, if you could answer a few of my questions, you'll give me a good
> start with PETSc. For the simple poisson problem that I am trying to
> implement, I have to discretize div(k grad u) integrated over each FV cell,
> where k is the known diffusivity, and u is the vector to solve for. 

Note that ex11 solves hyperbolic conservation laws, but you are solving
an elliptic equation.

> The cell integral is approximated as the sum of the fluxes (k grad u)
> in each face centroid multiplied by each surface area vector. In
> principle, I have all necessary information available in the DMPlex to
> assemble the FV matrix for div(k grad u), assuming an orthogonal grid
> for the beginning.  But I thought that the gradient coefficients
> should be available in the PETScFVFaceGeom.grad elements of the
> faceGeometry vector after using the methods
>
> DMPlexComputeGeometryFVM
> <https://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/DMPLEX/DMPlexComputeGeometryFVM.html#DMPlexComputeGeometryFVM>(DM
> <https://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/DM/DM.html#DM>
> dm, Vec <https://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/Vec/Vec.html#Vec>
> *cellgeom, Vec <https://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/Vec/Vec.html#Vec>
> *facegeom) and
> DMPlexComputeGradientFVM
> <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/DMPLEX/DMPlexComputeGradientFVM.html#DMPlexComputeGradientFVM>(DM
> <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/DM/DM.html#DM>
> dm, PetscFV <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/DM/PetscFV.html#PetscFV>
> fvm, Vec <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/Vec/Vec.html#Vec>
> faceGeometry, Vec
> <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/Vec/Vec.html#Vec>
> cellGeometry, DM
> <https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/DM/DM.html#DM>
> *dmGrad)
>
> But, while these calls fill in the cell and face centroids, volumes and
> normals, the PETScFVFaceGeom.grad elements of the faceGeometry vector are
> all zero. Am I misunderstanding the purpose of DMPlexComputeGradientFVM?

This routine is intended to do a conservative reconstruction of a
piecewise linear function from piecewise constant data.  Is that what
you want?

> (My second question is more general about the PETSc installation. When I
> configure PETSc with "--prefix=/somewhere --download-triangle
> --download-parmetis" etc., these extra libraries are built correctly during
> the make step, but they are not copied to /somewhere during the "make
> install" step. 

Where are they put during configure?

> Also the pkg-config files don't include the details about the extra
> libraries. Is it intended that one has to manually correct the install
> directory, or am I missing something during the configuration or
> installation steps?)

You shouldn't need that if linking with shared libraries (pkg-config
says not to list them), but you can use pkg-config --static to get the
transitive dependencies.
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