[petsc-users] Fwd: SNESSetFunction and MatMFFDSetFunction

[Dario Isola]

Dear, Barry and Jed,

Thanks for your replies.

We understand your doubts, so let me to put our question into context. 
In CFD it is standard practice to solve non-linear equations of 
conservation for steady flows by means of a inexact Newton method.  The 
original Jacobian matrix is modified by adding terms on the diagonal 
which are proportional to the Courant number and to the lumped mass 
matrix. This allows us to obtain two things, "relax" the solution update 
and increase the diagonal dominance of the matrix itself.

The latter is key when simple preconditioners are adopted, in our case 
point Jacobi or SOR.  Indeed, if the original matrix was to be used, the 
GMRES method would converge only on very regular meshes and only when 
adopting ILU preconditioners with a very high level of fill-in. As 
result a higher number of non-linear iterations is traded with a simpler 
linear system to be solved.

While exploring the SNES+MF capabilities we found out that we could 
successfully solve the linear system only with ILU(200) or so. Of course 
we do not want to touch the function used to evaluate the residual, 
which determines the final solution. However we think that a suitable 
modification of the function that Petsc differences to compute the 
matrix vector product would allow us to obtain a behavior similar to the 
inexact Newton method.

Best regards,
Dario


On 01/03/2014 12:32 PM, Song Gao wrote:
>
>
> ---------- Forwarded message ----------
> From: *Jed Brown* <jedbrown at mcs.anl.gov <mailto:jedbrown at mcs.anl.gov>>
> Date: Thu, Jan 2, 2014 at 10:20 AM
> Subject: Re: [petsc-users] SNESSetFunction and MatMFFDSetFunction
> To: Song Gao <song.gao2 at mail.mcgill.ca 
> <mailto:song.gao2 at mail.mcgill.ca>>, Barry Smith <bsmith at mcs.anl.gov 
> <mailto:bsmith at mcs.anl.gov>>
> Cc: petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>>
>
>
> Song Gao <song.gao2 at mail.mcgill.ca <mailto:song.gao2 at mail.mcgill.ca>> 
> writes:
>
> > Thanks, Barry.
> >
> > I mean 2) providing a function that I want PETSc to difference to 
> evaluate
> > the matrix vector product.
> >
> > I want to make a slight modification of the matrix after PETSc 
> evaluate the
> > matrix vector product.
>
> Performing a matrix-vector product is not supposed to modify the matrix.
> It's unlikely that you really want this.
>
>
> On Wed, Jan 1, 2014 at 3:01 PM, Barry Smith <bsmith at mcs.anl.gov 
> <mailto:bsmith at mcs.anl.gov>> wrote:
>
>
>     On Jan 1, 2014, at 11:09 AM, Song Gao <song.gao2 at mail.mcgill.ca
>     <mailto:song.gao2 at mail.mcgill.ca>> wrote:
>
>     > Dear all,
>     >
>     > Happy new year!
>     >
>     > I'm using the matrix-free method to solve NS equations. I call
>     the SNESSetFunction to set the RHS function. I think SNES also
>     uses that RHS function to evaluate the matrix vector product.
>
>        Yes, PETSc differences this function to evaluate the matrix
>     vector product.
>
>     >
>     > But I want to set one function to evaluate the residual, and
>     another different function to evaluate the matrix vector product.
>
>        Are you providing a function that
>
>         1) actually evaluates the matrix vector product or are you
>
>         2) providing a function that you want PETSc to difference to
>     evaluate the matrix vector product?
>
>     > How can I do that? Does MatMFFDSetFunction do this job?
>
>         For 2) yes, but if the function you provide is different than
>     the function provided with SNESSetFunction then the matrix-vector
>     product obtained from differencing it will not be “correct”
>     Jacobian for the SNESSetFunction() you are providing so I don’t
>     see why you would do it.
>
>        For 1) you should use MatCreateShell() and
>     MatShellSetOperation(mat,MATOP_MULT, ….) and then pass that matrix
>     to SNESSetJacobian(), then PETSc will use that “matrix” to do its
>     matrix-vector products.
>
>        Barry
>
>
>
>     >
>     > Any suggestion is appreciated. Thank you.
>     >
>     >
>     > Song
>
>

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