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

[Jed Brown]

On Thu, 29 Apr 2010 22:28:39 +0000, "Li, Zhisong (lizs)" <lizs at mail.uc.edu> wrote:
> I wonder if you mean the finite element method here. I am only
> planning FDM or FVM for my work. Actually we don't have any polynomial
> in incompressible N-S equations.

As Matt says, the convection term is quadratic, everything else is
linear.  You don't have an equation of state or a nonlinear rheology.
The true Jacobian is easy to assemble in this setting as long as you use
a linear spatial discretization.  If you use a nonlinear spatial
discretization such as WENO or a high-resolution TVD finite volume
method, then the true Jacobian is quite complicated to assemble and has
a huge stencil which will make it expensive to assemble and solve with.
You will get much better performance if you instead precondition with a
first-order upwind spatial discretization, with the action of the true
Jacobian applied matrix-free (e.g. -snes_mf_operator).

Jed