[petsc-users] about FD Jacobian for the new DAE solver
Li, Zhisong (lizs)
lizs at mail.uc.edu
Thu Apr 29 17:28:39 CDT 2010
Hi, Jed,
Thank you for your quick response.
but I don't understand why you said it's easy here. My professor got stuck on this problem:
>>It's pretty easy to code an analytic Jacobian for incompressible
>>Navier-Stokes since it's only a quadratic nonlinearity. But
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.
>From my understanding from ts/ex8, for example, the continuity equation with pressure term: F = d(p)/dt+ d(u)/dx+d(v)/dy, we need to compute J[0][0] = d(F)/d(p), J[1][0] = d(F)/d(u) and J[2][0] = d(F)/d(v). I speculate they are J[0][0] = 1/delta_t, J[1][0] = 1/delta_x and J[2][0] = 1/delta_y. Is this correct? And d(Lap(u))/d(u) might be more difficult.
This is not much about PETSc, but I hope you can still give me some help or suggest a book/ paper on this.
Thank you very much.
Zhisong Li
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