[petsc-users] Example for adaptive high-order FEM in PETSc

[Mark Adams]

On Sat, Jan 12, 2019 at 6:59 PM Manav Bhatia via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> I have been studying the source code and the manual entries in the
> documentation and have a better understanding of setting up a high-order DG
> analysis.
>
> I have been able to identify the routines that set the order of the space
> and its continuity (CG/DG).
>
> The following is still unclear and I would appreciate some guidance:
>
> — A implicit DG solve of the inviscid Euler equations would require
> Jacobian contributions from the Riemann Solver at element interfaces. I do
> not see the ability to define Jacobian contribution in
> PetscDSSetRiemannSolver. What would be the best approach to do this?
>

See
https://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/tutorials/ex11.c.html

The Riemann solver computes the flux and the Jacobian is assembled in PETSc.


>
> — It appears that the only two choices for polynomials are Lagrange and
> “simple”. I am not clear what the “simple” basis implies. Are these just
> powers of x, y and z?
>
> — Are Legendre polynomials available elsewhere in PETSc? I saw some
> mention of it in TS, but not in FE.
>
> Thanks,
> Manav
>
>
>
> > On Jan 12, 2019, at 2:46 AM, Manav Bhatia <bhatiamanav at gmail.com> wrote:
> >
> > While looking through some examples I see that both PetscDSSetJacobian
> and DMPlexSNESComputeJacobianFEM are being used to set the functions to
> evaluate the Jacobian contributions on each rank.
> >
> > This is my understanding after studying these (please correct if I am
> wrong):
> >
> > — The PetscDSSetJacobian (and its corresponding residual routine) does
> not seem to have the concept of an element. Instead, it provides the
> derivatives of solution at a point and requires that the coefficients for
> each form g_0, g_1, … be evaluated. Then, PETSc combines that in the
> background.
> >
> > — DMPlexSNESComputeJacobianFEM is a method that calls PetscDSSetJacobian
> to compute the Jacobian.
> >
> >
> > If this is correct, I am a bit confused about the following:
> >
> > — For a DG solve, I can see that PetscDSSetRiemannSolver can be used to
> compute the convective flux at the interface of two elements. However, I
> don’t see how the Jacobian contribution of this flux can be computed and
> added to the system Jacobian.
> >
> > — A more conventional FEM assembly iterates over elements, then over the
> quadrature points, where the shape functions and their derivatives are
> initialized and used for computation of residual and Jacobian. Is it
> possible to follow this procedure in PETSc with DMPlex/DMForest and still
> use multigrid? Is there an example that demonstrates this?
> >
> > — Is there some form of an index for elements that exist on the local
> processor that can be used to iterate on local elements?
> >
> >
> > I have tried to look, but could not find a document that outlines these
> concepts. Is there one that exists and I have missed it?
> >
> > I would greatly appreciate some direction.
> >
> > Regards,
> > Manav
> >
> >
> >
> >
> >> On Jan 11, 2019, at 10:03 PM, Manav Bhatia <bhatiamanav at gmail.com>
> wrote:
> >>
> >> Hi,
> >>
> >>  I am interested in setting up a high-order DG FEM solution with PETSc
> on an octree mesh with adaptivity and geometric multigrid preconditioning.
> Is there an example that demonstrates this with either DMForest or DMPlex.
> >>
> >> Thanks,
> >> Manav
> >>
> >>
> >
>
>
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