[petsc-users] about Finite Difference Jacobian Approximations

[yuxuan]

Hi all,
I am solving PDEs on a unstructured mesh by finite volume method. At beginning I was using matrix-free method. However, I found that 
PETSc provides some tools to help approximate the Jacobian matrices efficiently via finite differences. 

These tools are intended for use in certain situations where one is unable to compute Jacobian matrices ana- 

lytically, and matrix-free methods do not work well without a preconditioner, due to very poor conditioning.
in the Petsc manual
I started to use the Finite difference Jacobian approximations.
I customized my MyApproxJacobianStructure(), by the considering the neighbors of my unstructured mesh. I am using the tins. So if i and j are neighbors, I will call MatSetValue(*jac,i,j,zeros,INSERT_VALUES);
And finally, I got the structure of my Jacobain Matrix by MatFDColoringView().see the attachment. 
My question is whether my structure of the Jacobian matrix is good? And how to design preconditioned based on the structure of Jacobian matrix?


Thanks!


Cos
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