Hi Barry, Matt,
Barry, your solution worked, but I wanted to follow up on a few points on grid
sequencing
1. If, in using the grid sequence, there is no preallocation of the matrix,
does that mean I’m going to get hit (badly) with the mallocing as I increase
the number of levels?
2. In my problem, with real data, I see behavior like:
0 SNES Function norm 7.948742655505e-03
0 KSP Residual norm 3.666593515373e-03
1 KSP Residual norm 7.943650614441e-16
1 SNES Function norm 9.001557371893e-07
0 KSP Residual norm 8.814810163693e-06
1 KSP Residual norm 6.638031123907e-18
2 SNES Function norm 4.176927119066e-11
0 SNES Function norm 1.500187158175e+02
0 KSP Residual norm 1.006776821797e-01
1 KSP Residual norm 2.010368372645e-13
1 SNES Function norm 5.899853203939e-03
0 KSP Residual norm 1.752660743738e-02
1 KSP Residual norm 1.244868008219e-14
2 SNES Function norm 1.748583606371e-06
0 KSP Residual norm 4.933624839470e-06
1 KSP Residual norm 5.789658241868e-18
3 SNES Function norm 2.034638891687e-10
Where, when it gets to the first refinement, it’s not clear how much advantage
its taking of the coarser solution.
3. This problem is actually part of a continuation problem that roughly looks
like this
for( continuation parameter p = 0 to 1){
solve with parameter p_i using solution from p_{i-1},
}
What I would like to do is to start the solver, for each value of parameter p_i
on the coarse mesh, and then do grid sequencing on that. But it appears that
after doing grid sequencing on the initial p_0 = 0, the SNES is set to use the
finer mesh.
4. When I do SNESSolve(snes, NULL, U) with grid sequencing, U is not the
solution on the fine mesh. But what is it? Is it still the starting guess, or
is it the solution on the coarse mesh?
-gideon
> On Aug 28, 2015, at 6:20 AM, Matthew Knepley <[email protected]> wrote:
>
> On Thu, Aug 27, 2015 at 10:23 PM, Barry Smith <[email protected]
> <mailto:[email protected]>> wrote:
>
> > On Aug 27, 2015, at 10:15 PM, Gideon Simpson <[email protected]
> > <mailto:[email protected]>> wrote:
> >
> > That’s correct, I am not using the SNESGetDM. I suppose I could. Keep in
> > mind that I’m trying to solve, simultaneously, for the scalar parameters
> > and the vector field. I guess what I am unclear about is how DMRefine is
> > to know that the unknown associated with the scalar parameters can never be
> > coarsened out, but must be retained at all iterations.
>
> Nothing ever gets coarsened in grid sequencing, it only gets refined.
>
> The reason it knows not to "refine" the scalars is because the scalars
> are created with DMRedundant and the DMRedundant object knows that refinement
> means "leave as is, since there is no grid" while the DMDA knows it is a grid
> and knows how to refine itself. So when it "interpolates" the DMRedundant
> variables it just copies them (or multiples them by the matrix 1 which is
> just a copy).
>
> I think you might be misunderstanding the "scalars" part. He is solving a
> nonlinear eigenproblem (which he did not write down) for some variables. Then
> he
> uses those variable in the coupled diffusion equations he did write down. He
> has wrapped the whole problem in a SNES with 2 parts: the nonlinear
> eigenproblem
> and the diffusion equations. He uses DMComposite to deal with all the
> unknowns.
>
> I think Nonlinear Block Gauss-Siedel on the different problems would be a
> useful starting point, but we do not have that.
>
> Thanks,
>
> Matt
>
> >
> > Here is my form function. I can send more code if needed.
> >
>
> Just change the user->packer that you use to be the DM obtained with
> SNESGetDM()
>
>
> > /* Form the system of equations for computing a blowup solution*/
> > PetscErrorCode form_function(SNES snes, Vec U, Vec F, void *ctx){
> >
> > blowup_ctx *user = (blowup_ctx *) ctx;
> > PetscInt i;
> > PetscScalar dx, dx2, xmax,x;
> > PetscScalar u, v, f,g, ux, vx, uxx, vxx, fx,gx, fxx, gxx;
> > DMDALocalInfo info;
> > Vec p_vec, Q_vec, Fp_vec, FQ_vec;
> > PetscScalar *p_array, *Fp_array;
> > Q *Qvals, *FQvals;
> > PetscScalar Q2sig, W2sig;
> > PetscScalar a,a2, b, u0, sigma;
> >
> > dx = user->dx; dx2 = dx *dx;
> > xmax = user->xmax;
> > sigma = user->sigma;
> >
> > /* PetscPrintf(PETSC_COMM_SELF, " dx = %g, sigma = %g\n", dx, sigma); */
> >
> > /* Extract raw arrays */
> > DMCompositeGetLocalVectors(user->packer, &p_vec, &Q_vec);
> > DMCompositeGetLocalVectors(user->packer, &Fp_vec, &FQ_vec);
> >
> > DMCompositeScatter(user->packer, U, p_vec, Q_vec);
> > /* VecView(Q_vec, PETSC_VIEWER_STDOUT_SELF); */
> >
> > VecGetArray(p_vec,&p_array);
> > VecGetArray(Fp_vec,&Fp_array);
> >
> > DMDAVecGetArray(user->Q_dm, Q_vec, &Qvals);
> > DMDAVecGetArray(user->Q_dm, FQ_vec, &FQvals);
> >
> > DMDAGetLocalInfo(user->Q_dm, &info);
> >
> > a = p_array[0]; a2 = a*a;
> > b = p_array[1];
> > u0 = p_array[2];
> >
> > /* Set boundary conditions at the origin*/
> > if(info.xs ==0){
> > set_origin_bcs(u0, Qvals);
> > }
> > /* Set boundray conditions in the far field */
> > if(info.xs+ info.xm == info.mx <http://info.mx/>){
> > set_farfield_bcs(xmax,sigma, a, b, dx, Qvals,info.mx
> > <http://info.mx/>);
> > }
> >
> > /* Solve auxiliary equations */
> > if(info.xs ==0){
> > uxx = (2 * Qvals[0].u-2 * u0)/dx2;
> > vxx = (Qvals[0].v + Qvals[0].g)/dx2;
> > vx = (Qvals[0].v - Qvals[0].g)/(2*dx);
> > Fp_array[0] = Qvals[0].u - Qvals[0].f;
> > Fp_array[1] = -vxx - (1/a) * (.5/sigma) * u0;
> > Fp_array[2] = -uxx + (1/a2) * u0
> > + (1/a) * (-b * vx + PetscPowScalar(u0 * u0, sigma) * vx);
> > }
> >
> > /* Solve equations in the bulk */
> > for(i=info.xs; i < info.xs + info.xm;i++){
> >
> > u = Qvals[i].u;
> > v = Qvals[i].v;
> > f = Qvals[i].f;
> > g = Qvals[i].g;
> >
> > x = (i+1) * dx;
> >
> > Q2sig = PetscPowScalar(u*u + v*v,sigma);
> > W2sig= PetscPowScalar(f*f + g*g, sigma);
> >
> > ux = (Qvals[i+1].u-Qvals[i-1].u)/(2*dx);
> > vx = (Qvals[i+1].v-Qvals[i-1].v)/(2*dx);
> > fx = (Qvals[i+1].f-Qvals[i-1].f)/(2*dx);
> > gx = (Qvals[i+1].g-Qvals[i-1].g)/(2*dx);
> >
> > uxx = (Qvals[i+1].u+Qvals[i-1].u - 2 *u)/(dx2);
> > vxx = (Qvals[i+1].v+Qvals[i-1].v- 2 *v)/(dx2);
> > fxx = (Qvals[i+1].f+Qvals[i-1].f -2*f)/(dx2);
> > gxx = (Qvals[i+1].g+Qvals[i-1].g -2*g)/(dx2);
> >
> > FQvals[i].u = -uxx +1/a2 * u
> > + 1/a *(.5/sigma* v +x * vx- b* vx +Q2sig* vx);
> >
> > FQvals[i].v = -vxx +1/a2 * v
> > - 1/a *(.5/sigma * u +x * ux- b* ux +Q2sig* ux);
> >
> > FQvals[i].f = -fxx +1/a2 * f
> > + 1/a *(.5/sigma * g +x * gx+ b* gx -W2sig* gx);
> >
> > FQvals[i].g =-gxx +1/a2 * g
> > - 1/a *(.5/sigma * f +x * fx+ b* fx -W2sig* fx);
> > }
> >
> > /* Restore raw arrays */
> > VecRestoreArray(p_vec, &p_array);
> > VecRestoreArray(Fp_vec, &Fp_array);
> >
> > DMDAVecRestoreArray(user->Q_dm, Q_vec, &Qvals);
> > DMDAVecRestoreArray(user->Q_dm, FQ_vec, &FQvals);
> >
> > DMCompositeGather(user->packer,F,INSERT_VALUES, Fp_vec, FQ_vec);
> > DMCompositeRestoreLocalVectors(user->packer, &p_vec, &Q_vec);
> > DMCompositeRestoreLocalVectors(user->packer, &Fp_vec, &FQ_vec);
> >
> > return 0;
> > }
> >
> >
> > Here is the form function:
> >
> >
> >
> > -gideon
> >
> >> On Aug 27, 2015, at 11:09 PM, Barry Smith <[email protected]
> >> <mailto:[email protected]>> wrote:
> >>
> >>
> >> Can you send the code, that will be the easiest way to find the problem.
> >>
> >> My guess is that you have hardwired in your function/Jacobian computation
> >> the use of the original DM for computations instead of using the current
> >> DM (with refinement there will be a new DM on the second level different
> >> than your original DM). So what you need to do in writing your
> >> FormFunction and FormJacobian is to call SNESGetDM() to get the current DM
> >> and then use DMComputeGet... to access the individual DMDA and DMRedundent
> >> for the parts. I notice you have this user.Q_dm I bet inside your form
> >> functions you use this DM? You have to remove this logic.
> >>
> >> Barry
> >>
> >>> On Aug 27, 2015, at 9:42 PM, Gideon Simpson <[email protected]
> >>> <mailto:[email protected]>> wrote:
> >>>
> >>> I have it set up as:
> >>>
> >>> DMCompositeCreate(PETSC_COMM_WORLD, &user.packer);
> >>> DMRedundantCreate(PETSC_COMM_WORLD, 0, 3, &user.p_dm);
> >>> DMCompositeAddDM(user.packer,user.p_dm);
> >>> DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_GHOSTED,
> >>> nx, 4, 1, NULL, &user.Q_dm);
> >>> DMCompositeAddDM(user.packer,user.Q_dm);
> >>> DMCreateGlobalVector(user.packer,&U);
> >>>
> >>> where the user.packer structure has
> >>>
> >>> DM packer;
> >>> DM p_dm, Q_dm;
> >>>
> >>> Q_dm holds the field variables and p_dm holds the scalar values (the
> >>> nonlinear eigenvalues).
> >>>
> >>> Here are some of the errors that are generated:
> >>>
> >>> [0]PETSC ERROR: --------------------- Error Message
> >>> --------------------------------------------------------------
> >>> [0]PETSC ERROR: Argument out of range
> >>> [0]PETSC ERROR: New nonzero at (0,3) caused a malloc
> >>> Use MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE) to turn
> >>> off this check
> >>> [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html
> >>> <http://www.mcs.anl.gov/petsc/documentation/faq.html> for trouble
> >>> shooting.
> >>> [0]PETSC ERROR: Petsc Release Version 3.5.3, unknown
> >>> [0]PETSC ERROR: ./blowup_batch2 on a arch-macports named gs_air by gideon
> >>> Thu Aug 27 22:40:54 2015
> >>> [0]PETSC ERROR: Configure options --prefix=/opt/local
> >>> --prefix=/opt/local/lib/petsc --with-valgrind=0 --with-shared-libraries
> >>> --with-debugging=0 --with-c2html-dir=/opt/local --with-x=0
> >>> --with-blas-lapack-lib=/System/Library/Frameworks/Accelerate.framework/Versions/Current/Accelerate
> >>> --with-hwloc-dir=/opt/local --with-suitesparse-dir=/opt/local
> >>> --with-superlu-dir=/opt/local --with-metis-dir=/opt/local
> >>> --with-parmetis-dir=/opt/local --with-scalapack-dir=/opt/local
> >>> --with-mumps-dir=/opt/local --with-superlu_dist-dir=/opt/local
> >>> CC=/opt/local/bin/mpicc-mpich-mp CXX=/opt/local/bin/mpicxx-mpich-mp
> >>> FC=/opt/local/bin/mpif90-mpich-mp F77=/opt/local/bin/mpif90-mpich-mp
> >>> F90=/opt/local/bin/mpif90-mpich-mp COPTFLAGS=-Os CXXOPTFLAGS=-Os
> >>> FOPTFLAGS=-Os LDFLAGS="-L/opt/local/lib -Wl,-headerpad_max_install_names"
> >>> CPPFLAGS=-I/opt/local/include CFLAGS="-Os -arch x86_64" CXXFLAGS=-Os
> >>> FFLAGS=-Os FCFLAGS=-Os F90FLAGS=-Os PETSC_ARCH=arch-macports
> >>> --with-mpiexec=mpiexec-mpich-mp
> >>> [0]PETSC ERROR: #1 MatSetValues_MPIAIJ() line 530 in
> >>> /opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_release_tarballs_ports_math_petsc/petsc/work/v3.5.3/src/mat/impls/aij/mpi/mpiaij.c
> >>> [0]PETSC ERROR: [1]PETSC ERROR: --------------------- Error Message
> >>> --------------------------------------------------------------
> >>> [1]PETSC ERROR: Argument out of range
> >>> [1]PETSC ERROR: Inserting a new nonzero (40003, 0) into matrix
> >>> [1]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html
> >>> <http://www.mcs.anl.gov/petsc/documentation/faq.html> for trouble
> >>> shooting.
> >>> [1]PETSC ERROR: Petsc Release Version 3.5.3, unknown
> >>> [1]PETSC ERROR: ./blowup_batch2 on a arch-macports named gs_air by gideon
> >>> Thu Aug 27 22:40:54 2015
> >>> [1]PETSC ERROR: Configure options --prefix=/opt/local
> >>> --prefix=/opt/local/lib/petsc --with-valgrind=0 --with-shared-libraries
> >>> --with-debugging=0 --with-c2html-dir=/opt/local --with-x=0
> >>> --with-blas-lapack-lib=/System/Library/Frameworks/Accelerate.framework/Versions/Current/Accelerate
> >>> --with-hwloc-dir=/opt/local --with-suitesparse-dir=/opt/local
> >>> --with-superlu-dir=/opt/local --with-metis-dir=/opt/local
> >>> --with-parmetis-dir=/opt/local --with-scalapack-dir=/opt/local
> >>> --with-mumps-dir=/opt/local --with-superlu_dist-dir=/opt/local
> >>> CC=/opt/local/bin/mpicc-mpich-mp CXX=/opt/local/bin/mpicxx-mpich-mp
> >>> FC=/opt/local/bin/mpif90-mpich-mp F77=/opt/local/bin/mpif90-mpich-mp
> >>> F90=/opt/local/bin/mpif90-mpich-mp COPTFLAGS=-Os CXXOPTFLAGS=-Os
> >>> FOPTFLAGS=-Os LDFLAGS="-L/opt/local/lib -Wl,-headerpad_max_install_names"
> >>> CPPFLAGS=-I/opt/local/include CFLAGS="-Os -arch x86_64" CXXFLAGS=-Os
> >>> FFLAGS=-Os FCFLAGS=-Os F90FLAGS=-Os PETSC_ARCH=arch-macports
> >>> --with-mpiexec=mpiexec-mpich-mp
> >>> [1]PETSC ERROR: #1 MatSetValues_MPIAIJ() line 561 in
> >>> /opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_release_tarballs_ports_math_petsc/petsc/work/v3.5.3/src/mat/impls/aij/mpi/mpiaij.c
> >>> [1]PETSC ERROR: #2 MatSetValues() line 1135 in
> >>> /opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_release_tarballs_ports_math_petsc/petsc/work/v3.5.3/src/mat/interface/matrix.c
> >>>
> >>>
> >>>
> >>> -gideon
> >>>
> >>>> On Aug 27, 2015, at 10:37 PM, Barry Smith <[email protected]
> >>>> <mailto:[email protected]>> wrote:
> >>>>
> >>>>
> >>>> We need the full error message.
> >>>>
> >>>> But are you using a DMDA for the scalars? You should not be, you should
> >>>> be using a DMRedundant for the scalars.
> >>>>
> >>>> Barry
> >>>>
> >>>> Though you should not get this error even if you are using a DMDA there.
> >>>>
> >>>>> On Aug 27, 2015, at 9:32 PM, Gideon Simpson <[email protected]
> >>>>> <mailto:[email protected]>> wrote:
> >>>>>
> >>>>> I’m getting the following errors:
> >>>>>
> >>>>> [1]PETSC ERROR: Argument out of range
> >>>>> [1]PETSC ERROR: Inserting a new nonzero (40003, 0) into matrix
> >>>>>
> >>>>> Could this have to do with me using the DMComposite with one da holding
> >>>>> the scalar parameters and the other holding the field variables?
> >>>>>
> >>>>> -gideon
> >>>>>
> >>>>>> On Aug 27, 2015, at 10:15 PM, Matthew Knepley <[email protected]
> >>>>>> <mailto:[email protected]>> wrote:
> >>>>>>
> >>>>>> On Thu, Aug 27, 2015 at 9:11 PM, Gideon Simpson
> >>>>>> <[email protected] <mailto:[email protected]>> wrote:
> >>>>>> HI Barry,
> >>>>>>
> >>>>>> Nope, I’m not doing any grid sequencing. Clearly that makes a lot of
> >>>>>> sense, to solve on a spatially coarse mesh for the field variables,
> >>>>>> interpolate onto the finer mesh, and then solve again. I’m not
> >>>>>> entirely clear on the practical implementation
> >>>>>>
> >>>>>> SNES should do this automatically using -snes_grid_sequence <k>. If
> >>>>>> this does not work, complain. Loudly.
> >>>>>>
> >>>>>> Matt
> >>>>>>
> >>>>>> -gideon
> >>>>>>
> >>>>>>> On Aug 27, 2015, at 10:02 PM, Barry Smith <[email protected]
> >>>>>>> <mailto:[email protected]>> wrote:
> >>>>>>>
> >>>>>>>
> >>>>>>> Gideon,
> >>>>>>>
> >>>>>>> Are you using grid sequencing? Simply solve on a coarse grid,
> >>>>>>> interpolate u1 and u2 to a once refined version of the grid and use
> >>>>>>> that plus the mu lam as initial guess for the next level. Repeat to
> >>>>>>> as fine a grid as you want. You can use DMRefine() and
> >>>>>>> DMGetInterpolation() to get the interpolation needed to interpolate
> >>>>>>> from the coarse to finer mesh.
> >>>>>>>
> >>>>>>> Then and only then you can use multigrid (with or without fieldsplit)
> >>>>>>> to solve the linear problems for finer meshes. Once you have the grid
> >>>>>>> sequencing working we can help you with this.
> >>>>>>>
> >>>>>>> Barry
> >>>>>>>
> >>>>>>>> On Aug 27, 2015, at 7:00 PM, Gideon Simpson
> >>>>>>>> <[email protected] <mailto:[email protected]>> wrote:
> >>>>>>>>
> >>>>>>>> I’m working on a problem which, morally, can be posed as a system of
> >>>>>>>> coupled semi linear elliptic PDEs together with unknown nonlinear
> >>>>>>>> eigenvalue parameters, loosely, of the form
> >>>>>>>>
> >>>>>>>> -\Delta u_1 + f(u_1, u_2) = lam * u1 - mu * du2/dx
> >>>>>>>> -\Delta u_2 + g(u_1, u_2) = lam * u2 + mu * du1/dx
> >>>>>>>>
> >>>>>>>> Currently, I have it set up with a DMComposite with two sub da’s,
> >>>>>>>> one for the parameters (lam, mu), and one for the vector field (u_1,
> >>>>>>>> u_2) on the mesh. I have had success in solving this as a fully
> >>>>>>>> coupled system with SNES + sparse direct solvers (MUMPS, SuperLU).
> >>>>>>>>
> >>>>>>>> Lately, I am finding that, when the mesh resolution gets fine enough
> >>>>>>>> (i.e. 10^6-10^8 lattice points), my SNES gets stuck with the
> >>>>>>>> function norm = O(10^{-4}), eventually returning reason -6 (failed
> >>>>>>>> line search).
> >>>>>>>>
> >>>>>>>> Perhaps there is another way around the above problem, but one thing
> >>>>>>>> I was thinking of trying would be to get away from direct solvers,
> >>>>>>>> and I was hoping to use field split for this. However, it’s a bit
> >>>>>>>> beyond what I’ve seen examples for because it has 2 types of
> >>>>>>>> variables: scalar parameters which appear globally in the system and
> >>>>>>>> vector valued field variables. Any suggestions on how to get
> >>>>>>>> started?
> >>>>>>>>
> >>>>>>>> -gideon
> >>>>>>>>
> >>>>>>>
> >>>>>>
> >>>>>>
> >>>>>>
> >>>>>>
> >>>>>> --
> >>>>>> 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
> >>>>>
> >>>>
> >>>
> >>
> >
>
>
>
>
> --
> 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
