[petsc-users] SNES convergence conditons

[Matthew Knepley]

On Mon, Jan 20, 2014 at 12:46 PM, Dharmendar Reddy
<dharmareddy84 at gmail.com>wrote:

> Hello,
>         I have a doubt regarding error condition for SNES. For F(X) =
> 0, where X is a vector X = [x1 x2 x3 ....]', my understanding is, for
> convergence criteria based on X, SNES checks for


Convergence criteria should depend on what physics you want to resolve,
the experiments you want to compare with, etc. I don't think we can tell you
what to use. However,

  a) Your use of dX below is strange. Tolerances like these are vulnerable
to
       stagnation of the iteration and I would never use them. PETSc uses
something like

      norm2(F(x^k))/norm2(F(x^0)) < relTol || norm2(F(x^k)) < absTol

      which will tell you whether you have actually solved the equations

  b) The choice of norm depends on what needs to be accurate. norm2 is
appropriate
       for energies (and other quadratic things), whereas norm1 makes sense
for mass
       (and additive things). I don't have a physical motivation for
norm_inf.

  c) You can always set your own convergence test

   Matt


>
1) norm2(dX)/(rTol*norm2(X) + absTol) < 1 and converged if true.
>
> I have two other options to consider,
>
> 2)  1/N * norm1 ( dX/ (rTol*abs(X)+aTol)) < 1 where N is the size of (X)
>
> 3)  norm_infinity ( dX/  (rTol*abs(X)+aTol) ) < 1
>
> Which is a better option ? rather how should one decide which one to
> use ? I am trying to solve the semiconductor transport equations
> (poisson + particle convection). I use a comercial solver called
> synopsys TCAD, and it uses option 2 to test the convergence along with
> option 1 applied for testing convergence based on Function norm.
>
> I am inclined towards option 3 is more local and a stronger condition than
> 1.
>
> If i solve a set of couple equation
>
> F1(X1,X2,X3) = 0,
> F2(X1,X2,X3) = 0,
> F3(X1,X2,X3) = 0
>
> How do i use different absTol for X1, X2, and X3 to test the
> convergence criteria.
>
> Thanks
> Reddy
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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