[petsc-users] A question on finite difference Jacobian

[Barry Smith]

> On Oct 6, 2015, at 3:29 PM, Zou (Non-US), Ling <ling.zou at inl.gov> wrote:
> 
> Hi All,
> 
> If the non-zero pattern of a finite difference Jacobian needs 20 colors to color it (20 comes from MatFDColoringView, the non-zero pattern is pre-determined from mesh connectivity), is it true that PETSc needs 40 functions evaluation to get the full Jacobian matrix filled? This is because that a perturbation per color needs two function evaluation according to PETSc manual (ver 3.6, page 123, equations shown in the middle of the page).
> But I only see 20 function evaluations. I probably have some misunderstanding somewhere. Any suggestions?

   PETSc uses forward differencing to compute the derivatives, hence it needs a single function evaluation at the given point (which has almost always been previously computed in Newton's method) and then one function evaluation for each color. This is why it reports 20 function evaluations.

  Barry


> 
> Ling