[petsc-users] Preconditioning in SNES

[Konstantinos Kontzialis]

On 11/01/2011 05:24 PM, petsc-users-request at mcs.anl.gov wrote:
> Preconditioning in SNES

Deall all,

1. I use 3.1 version of petsc.
2. I run the problem with snes_fd and pc_type lu
3. I use a nondimensional form of the NS equations
4. I do not specify any user defined procedure for applying the 
preconditioner. I leave petsc to deal with this.

With snes_fd I got the following results:

Timestep   0: dt = 0.002, T = 0, Res[rho] = 1.06871e-16, Res[rhou] = 
0.00215523, Res[rhov] = 1.61374e-08, Res[E] = 6.17917e-07, CFL = 399.998

/*********************Stage 1 of SSPIRK (6,4)******************/

   0 SNES Function norm 1.153030915909e-02
     0 KSP preconditioned resid norm 1.153030915909e-02 true resid norm 
1.153030915909e-02 ||A||/||Ax|| 1.000000000000e+00
     1 KSP preconditioned resid norm 1.998438714390e-11 true resid norm 
1.998438714940e-11 ||Ae||/||Ax|| 1.733204797344e-09
Linear solve converged due to CONVERGED_RTOL iterations 1
   1 SNES Function norm 1.908346652619e-08
     0 KSP preconditioned resid norm 1.908346652619e-08 true resid norm 
1.908346652619e-08 ||Ae||/||Ax|| 1.000000000000e+00
     1 KSP preconditioned resid norm 1.407495233141e-08 true resid norm 
2.936727417791e-08 ||Ae||/||Ax|| 1.538885722759e+00
     2 KSP preconditioned resid norm 1.983096664116e-16 true resid norm 
4.111894600521e-03 ||Ae||/||Ax|| 2.154689555421e+05
Linear solve converged due to CONVERGED_RTOL iterations 2
   2 SNES Function norm 2.818079289176e-03

I think I need first to clarify the following.:

My function for computing the residual of the system has the following form:

F(u) = Mu + R(u),

where M is the mass matrix of the system and R(u) the residual and u is 
the solution. If I use snes_mf do I really get:

F'(u) = M+R'(u),

during the solution of the linear system?

Thanks,

Kostas