[petsc-users] Parallel TS for ODE

[Matthew Knepley]

On Tue, Apr 20, 2021 at 9:36 AM Francesco Brarda <brardafrancesco at gmail.com>
wrote:

> Hi!
> I tried to implement the SIR model taking into account the fact that I
> will only use 3 MPI ranks at this moment.
> I built vectors and matrices following the examples already available. In
> particular, I defined the functions required similarly (RHSFunction,
> IFunction, IJacobian), as follows:
>

I don't think this makes sense. You use "mybase" to distinguish between 3
procs, which would indicate that each procs has only
1 degree of freedom. However, you use x[1] on each proc, indicating it has
at least 2 dofs.

  Thanks,

     Matt


> static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
> {
>   PetscErrorCode    ierr;
>   AppCtx            *appctx = (AppCtx*) ctx;
>   PetscScalar       f;//, *x_localptr;
>   const PetscScalar *x;
>   PetscInt          mybase;
>
>   PetscFunctionBeginUser;
>   ierr = VecGetOwnershipRange(X,&mybase,NULL);CHKERRQ(ierr);
>   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
>   if (mybase == 0) {
>     f    = (PetscScalar) (-appctx->p1*x[0]*x[1]/appctx->N);
>     ierr = VecSetValues(F,1,&mybase,&f,INSERT_VALUES);
>   }
>   if (mybase == 1) {
>     f    = (PetscScalar) (appctx->p1*x[0]*x[1]/appctx->N-appctx->p2*x[1]);
>     ierr = VecSetValues(F,1,&mybase,&f,INSERT_VALUES);
>   }
>   if (mybase == 2) {
>     f    = (PetscScalar) (appctx->p2*x[1]);
>     ierr = VecSetValues(F,1,&mybase,&f,INSERT_VALUES);
>   }
>   ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
>   ierr = VecAssemblyBegin(F);CHKERRQ(ierr);
>   ierr = VecAssemblyEnd(F);CHKERRQ(ierr);
>   PetscFunctionReturn(0);
> }
>
>
> Whilst for the Jacobian I did:
>
>
> static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal
> a,Mat A,Mat B,void *ctx)
> {
>   PetscErrorCode    ierr;
>   AppCtx            *appctx = (AppCtx*) ctx;
>   PetscInt          mybase, rowcol[] = {0,1,2};
>   const PetscScalar *x;
>
>   PetscFunctionBeginUser;
>   ierr = MatGetOwnershipRange(B,&mybase,NULL);CHKERRQ(ierr);
>   ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
>   if (mybase == 0) {
>     const PetscScalar J[] = {a + appctx->p1*x[1]/appctx->N,
> appctx->p1*x[0]/appctx->N, 0};
>     ierr =
> MatSetValues(B,1,&mybase,3,rowcol,J,INSERT_VALUES);CHKERRQ(ierr);
>   }
>   if (mybase == 1) {
>     const PetscScalar J[] = {- appctx->p1*x[1]/appctx->N, a -
> appctx->p1*x[0]/appctx->N + appctx->p2, 0};
>     ierr =
> MatSetValues(B,1,&mybase,3,rowcol,J,INSERT_VALUES);CHKERRQ(ierr);
>   }
>   if (mybase == 2) {
>     const PetscScalar J[] = {0, - appctx->p2, a};
>     ierr =
> MatSetValues(B,1,&mybase,3,rowcol,J,INSERT_VALUES);CHKERRQ(ierr);
>   }
>   ierr    = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
>
>   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
>   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
>   if (A != B) {
>     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
>     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
>   }
>   PetscFunctionReturn(0);
> }
>
> This code does not provide the correct result, that is, the solution is
> the initial condition, either using implicit or explicit methods. Is the
> way I defined these objects wrong? How can I fix it?
> I also tried to print the Jacobian with the following commands but it does
> not work (blank rows and error message). How should I print the Jacobian?
>
> ierr = TSGetIJacobian(ts,NULL,&K, NULL, NULL); CHKERRQ(ierr);
> ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
> ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
> ierr = MatView(K,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
>
>
> I would very much appreciate any kind of help or advice.
> Best,
> Francesco
>
> Il giorno 2 apr 2021, alle ore 04:45, Barry Smith <bsmith at petsc.dev> ha
> scritto:
>
>
>
> On Apr 1, 2021, at 9:17 PM, Zhang, Hong via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>
>
> On Mar 31, 2021, at 2:53 AM, Francesco Brarda <brardafrancesco at gmail.com>
> wrote:
>
> Hi everyone!
>
> I am trying to solve a system of 3 ODEs (a basic SIR model) with TS.
> Sequentially works pretty well, but I need to switch it into a
> parallel version.
> I started working with TS not very long time ago, there are few questions
> I’d like to share with you and if you have any advices I’d be happy to hear.
> First of all, do I need to use a DM object even if the model is only time
> dependent? All the examples I found were using that object for the other
> variable when solving PDEs.
>
>
> Are you considering SIR on a spatial domain? If so, you can parallelize
> your model in the spatial domain using DM. Splitting the three variables in
> the ODE among processors would not scale.
>
>
>  Even though it will not scale and will deliver slower performance it is
> completely possible for you to solve the 3 variable problem using 3 MPI
> ranks. Or 10 mpi ranks. You would just create vectors/matrices with 1
> degree of freedom for the first three ranks and no degrees of freedom for
> the later ranks. During your function evaluation (and Jacobian evaluation)
> for TS you will need to set up the appropriate communication to get the
> values you need on each rank to evaluate the parts of the function
> evaluation needed by that rank. This is true for parallelizing any
> computation.
>
>  Barry
>
>
>
>
>
> Hong (Mr.)
>
> When I preallocate the space for the Jacobian matrix, is it better to
> decide the local or global space?
>
> Best,
> Francesco
>
>
>

-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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