[petsc-users] What is the difference between these two approaches?

[Matthew Knepley]

I am confused by b). If they both converge, how can the answers be
different?

  Matt

On Mon, Feb 8, 2010 at 3:13 PM, (Rebecca) Xuefei YUAN
<xy2102 at columbia.edu>wrote:

> Dear all,
>
> I do have an PDE-constrained optimization problem:
>
> F1(phi(x,y),c) = L(phi(x,y)) + rho(s1(x,y),s2(x,y)) = 0 (1)
> F2(phi(x,y),c) = int_{domain}(c*rho(s1(x,y),s2(x,y)) - 1.0)dxdy = 0 (2)
>
> where phi(x,y) is defined at each grid point and c is a scalar parameter
> that satisfying the equation (2).
>
> I have two pieces of codes to solve them by different approaches.
>
> The first approach is to use DMComposite() to manage unknowns and solve
> F1&F2 at the same time, and it calls DMMGSolve() once.
>
> The second approach is to solve F1 with a guess c for some number(i.e. 1)
> times of nonlinear and linear iteration, and then update c from F2. Solve F1
> again with updated c till some conditions satisfied, for example,
>
> if (cres<1e-10){CONTINUE=PETSC_FALSE;} // update on c
> if (functionNorm<1e-10){CONTINUE=PETSC_FALSE;}//residual function norm
> if (reason>0){CONTINUE=PETSC_FALSE;}//snes_converged_reason
> if (totalNumberOfNonlinearIterations>50){CONTINUE=PETSC_FALSE;}
>
> In this approach, DMMGSolve() was called more than once.
>
> Although these two approaches convergence, the results are quite different.
>
> My understanding is that
> a) approach one updates c in each linear iteration, but approach two
> updates c
> only after several (i.e. 1) nonlinear iterations.
>
> ierr = DMMGSolve(dmmg);CHKERRQ(ierr);
> parameters->c = parameters->integration/area;
>
> b) the results from two approaches should be the same or very close to each
> other but due to some reasons, they are not.
>
> c) three different examples are tested by these two approaches, two are
> good, but one is bad. The bad one is different from the other two because
> the solution has large gradient at some points.
>
> d) the shortcoming of approach one is PETSc has not ready for assemble a
> Jacobian for object DMComposite, so the second approach is able to write an
> analytic Jacobian.
>
> Any thoughts about how to debug or compare these two approaches is
> appreciate!~
>
>
> Thanks a ton!
>
> Rebecca
>
>
>
>
>
> --
> (Rebecca) Xuefei YUAN
> Department of Applied Physics and Applied Mathematics
> Columbia University
> Tel:917-399-8032
> www.columbia.edu/~xy2102 <http://www.columbia.edu/%7Exy2102>
>
>


-- 
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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