[petsc-users] PetscFV and TS implicit

[Thibault Bridel-Bertomeu]

Hi,

Thanks Matthew and Jed for your input.
I indeed envision an implicit solver in the sense Jed mentioned - Jiri
Blazek's book is a nice intro to this concept.

Matthew, I do not know exactly what to change right now because although I
understand globally what the DMPlexComputeXXXX_Internal methods do, I
cannot say for sure line by line what is happening.
In a structured code, I have a an implicit FVM solver with PETSc but I do
not use any of the FV structure, not even a DM - I just use C arrays that I
transform to PETSc Vec and Mat and build my IJacobian and my preconditioner
and gives all that to a TS and it runs. I cannot figure out how to do it
with the FV and the DM and all the underlying "shortcuts" that I want to
use.

Here is the top method for the structured code :

int total_size = context.npoints * solver->nvars
ierr = TSSetRHSFunction(ts,PETSC_NULL,PetscRHSFunctionImpl,&context);
CHKERRQ(ierr);
SNES snes;
KSP ksp;
PC pc;
SNESType snestype;
ierr = TSGetSNES(ts,&snes); CHKERRQ(ierr);
ierr = SNESGetType(snes,&snestype); CHKERRQ(ierr);

flag_mat_a = 1;
ierr = MatCreateShell(MPI_COMM_WORLD,total_size,total_size,PETSC_DETERMINE,
PETSC_DETERMINE,&context,&A); CHKERRQ(ierr);
context.jfnk_eps = 1e-7;
ierr = PetscOptionsGetReal(NULL,NULL,"-jfnk_epsilon",&context.jfnk_eps,NULL);
CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_MULT,(void (*)(void))
PetscJacobianFunction_JFNK); CHKERRQ(ierr);
ierr = MatSetUp(A); CHKERRQ(ierr);

context.flag_use_precon = 0;
ierr = PetscOptionsGetBool(PETSC_NULL,PETSC_NULL,"-with_pc",(PetscBool*)(&
context.flag_use_precon),PETSC_NULL); CHKERRQ(ierr);

/* Set up preconditioner matrix */
flag_mat_b = 1;
ierr = MatCreateAIJ(MPI_COMM_WORLD,total_size,total_size,PETSC_DETERMINE,
PETSC_DETERMINE,
(solver->ndims*2+1)*solver->nvars,NULL,
2*solver->ndims*solver->nvars,NULL,&B); CHKERRQ(ierr);
ierr = MatSetBlockSize(B,solver->nvars);
/* Set the RHSJacobian function for TS */
ierr = TSSetIJacobian(ts,A,B,PetscIJacobian,&context); CHKERRQ(ierr);

Thibault Bridel-Bertomeu
—
Eng, MSc, PhD
Research Engineer
CEA/CESTA
33114 LE BARP
Tel.: (+33)557046924
Mob.: (+33)611025322
Mail: thibault.bridelbertomeu at gmail.com


Le jeu. 20 août 2020 à 18:43, Jed Brown <jed at jedbrown.org> a écrit :

> Matthew Knepley <knepley at gmail.com> writes:
>
> > I could never get the FVM stuff to make sense to me for implicit methods.
> > Here is my problem understanding. If you have an FVM method, it decides
> > to move "stuff" from one cell to its neighboring cells depending on the
> > solution to the Riemann problem on each face, which computed the flux.
> This
> > is
> > fine unless the timestep is so big that material can flow through into
> the
> > cells beyond the neighbor. Then I should have considered the effect of
> the
> > Riemann problem for those interfaces. That would be in the Jacobian, but
> I
> > don't know how to compute that Jacobian. I guess you could do everything
> > matrix-free, but without a preconditioner it seems hard.
>
> So long as we're using method of lines, the flux is just instantaneous
> flux, not integrated over some time step.  It has the same meaning for
> implicit and explicit.
>
> An explicit method would be unstable if you took such a large time step
> (CFL) and an implicit method will not simultaneously be SSP and higher than
> first order, but it's still a consistent discretization of the problem.
>
> It's common (done in FUN3D and others) to precondition with a first-order
> method, where gradient reconstruction/limiting is skipped.  That's what I'd
> recommend because limiting creates nasty nonlinearities and the resulting
> discretizations lack h-ellipticity which makes them very hard to solve.
>
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