[petsc-users] about FD Jacobian for the new DAE solver

[Jed Brown]

On Thu, 29 Apr 2010 21:08:38 +0000, "Li, Zhisong (lizs)" <lizs at mail.uc.edu> wrote:
>  Hi,
> 
> Last time I was suggested by Jed using the DAE solver to build my
> nonlinear CFD code based on TS. For incompressible N-S equations, I
> think it's difficult to derive the analytical Jacobian formulation,
> and we need a finite difference approximation or matrix-free method.

It's pretty easy to code an analytic Jacobian for incompressible
Navier-Stokes since it's only a quadratic nonlinearity.  But 

> What I previously done was integrating the incompressible N-S equations into tutorial code ts/ex7.c  . It simply uses an argument "TSDefaultComputeJacobianColor" to finish the Jacobian issue. When I switch to TSSetIFunction() and TSSetIJacobian(), this argument doesn't work anymore. And if I remove all Jacobian-related lines and use -snes_mf command option, it prompts out error message "Must Set Jacobian!". Do you know how to resolve this for both methods?

If you use -snes_mf or -snes_fd, then you can call TSSetIJacobian() and
not provide a function.  If you are using petsc-dev, then
ts/examples/tutorials/ex10.c has the following method (which is also
more efficient than TSDefaultComputeJacobianColor).

      SNES       snes;
      ISColoring iscoloring;
      ierr = TSGetSNES(ts,&snes);
      ierr = DAGetColoring(rd->da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);CHKERRQ(ierr);
      ierr = MatFDColoringCreate(B,iscoloring,&matfdcoloring);CHKERRQ(ierr);
      ierr = ISColoringDestroy(iscoloring);CHKERRQ(ierr);
      ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode(*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
      ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
      ierr = SNESSetJacobian(snes,A,B,SNESDefaultComputeJacobianColor,matfdcoloring);CHKERRQ(ierr);

But it looks like TSPSEUDO will currently overwrite this (the other
integrators deal with this correctly).  I'll push a fix shortly.

Jed