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

[(Rebecca) Xuefei YUAN]

That is also confusing me when running this bad example. The good  
examples have matched solutions, but this bad one does not. I do not  
know what is wrong and where is the difference coming from?




Quoting Matthew Knepley <knepley at gmail.com>:

> 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
>



-- 
(Rebecca) Xuefei YUAN
Department of Applied Physics and Applied Mathematics
Columbia University
Tel:917-399-8032
www.columbia.edu/~xy2102