[petsc-users] Finite difference Jacobian in TS context

[Oleksandr Koshkarov]

Thank you. A little clarification:

>     The above uses matrix-free to do matrix-vector products for linear system but constructs the preconditioner by building the Jacobian via differencing and then using that matrix to build the preconditioner.
So SNESComputeJacobianDefaultColor will use memory (construct Jacobian) 
even if preconditioning is set to PCNONE and J=NULL? (that is what I saw 
in my example)

>     This does not build the Jacobian (only has matrix free matrix vector products) so requires much less memory but likely for large problem sizes the linear system solve will be slow (require many iterations) or won't converge at all.   The conditioning of the linear system depends on the exact problem you are solving and the type of discretization you are using. There is no easy rules that always apply but for most discretizations of PDEs the number of iterations needed by the linear solver increases with the problem sizes. This means for most large problems matrix-free (without building any sort of jacobean and preconditioner) is impractical and one needs to pay the price of using more memory to get reasonable convergence.
So the following command  ignores precoditioning? Can I still use 
something like PCSHELL?

SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,0);


p.s. for my problems if probably be unrealistic to construct Jacobian 
(state size will start from N > 1000^4).

Thank you,

Oleksandr.


On 04/29/2018 05:26 PM, Smith, Barry F. wrote:
>
>> On Apr 29, 2018, at 5:40 PM, Oleksandr Koshkarov <olk548 at mail.usask.ca> wrote:
>>
>> Dear All,
>>
>> sorry for spam because of my poor PETSc knowledge (I am just starting with this nice framework).
>>
>> I think, I figured part of it out. However, I want to point that src/ts/examples/tutorials/ex15.c is misleading. (or maybe it is a bug?)
>>
>> in this example we have
>>
>> TSGetSNES(ts,&snes);
>> MatCreateSNESMF(snes,&Jmf);
>> SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);
>>
>> // or this: SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);
>>
>> which implies (I think) that Jacobian would be matrix free. And if one would use PCNONE for preconditioning the matrix would never be allocated. However, it seems in reality it allocates matrix.
>     The above uses matrix-free to do matrix-vector products for linear system but constructs the preconditioner by building the Jacobian via differencing and then using that matrix to build the preconditioner.
>
>> To avoid it, I used
>>
>> MatCreateSNESMF(snes,&J);
>>
>> SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,0);
>>
>> which seems to work fine. I am not sure I fully understand the difference and i have zero intuition and I also have no idea what happens with preconditioning in this case. If someone have some useful comets, please share :) (I read the relevant section in PETSc manual, but still not fully understanding what I should use when)
>      This does not build the Jacobian (only has matrix free matrix vector products) so requires much less memory but likely for large problem sizes the linear system solve will be slow (require many iterations) or won't converge at all.   The conditioning of the linear system depends on the exact problem you are solving and the type of discretization you are using. There is no easy rules that always apply but for most discretizations of PDEs the number of iterations needed by the linear solver increases with the problem sizes. This means for most large problems matrix-free (without building any sort of jacobean and preconditioner) is impractical and one needs to pay the price of using more memory to get reasonable convergence.
>
>    Barry
>
>> Thank you and again sorry for the spam,
>> Oleksandr.
>>
>> On 04/28/2018 07:20 PM, Smith, Barry F. wrote:
>>> ~/Src/petsc/src/ts/examples/tutorials
>>> $ grep SNESComputeJacobianDefaultColor *.c
>>> ex10.c:    ierr = SNESSetJacobian(snes,A,B,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr);
>>> ex15.c:      ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr);
>>> ex17.c:    ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr);
>>>
>>>     I don't think you need to explicitly create the MatFDColoring object.
>>>
>>>     Please take a look at ex15.c and see if you can get it working like that example. If that doesn't work let us know and we can take a closer look at it.
>>>
>>>
>>>     Barry
>>>
>>>
>>>> On Apr 28, 2018, at 8:05 PM, Oleksandr Koshkarov <olk548 at mail.usask.ca> wrote:
>>>>
>>>> Hello All,
>>>>
>>>> I hope someone can help :) I think I am doing something wrong, but cannot understand what. I have a huge time dependent system with 3d DMDA data structure and I am evolving it with explicit Runge-Kutta by using TS and basically only using "TSSetRHSFunction". Now I want to repeat it with implicit time stepper (for now Crank-Nicolson) and I am trying to provide finite difference Jacobian and I am failing miserably. I also cannot find appropriate example in PETSc tutorial (if you can point me to working example, it would be great).
>>>>
>>>> Here is my best attempt (what wrong with it?):
>>>>
>>>>    DMDACreate3d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC,
>>>>             DMDA_STENCIL_STAR,
>>>>             NX, NY, NZ,
>>>>             PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE,
>>>>             2*3+NC*NS,
>>>>             1,
>>>>             NULL,  NULL, NULL,  &da);
>>>>    DMSetUp(da);
>>>>    DMCreateGlobalVector(da,&x);
>>>>    TSCreate(PETSC_COMM_WORLD,&ts);
>>>>    TSSetProblemType(ts,TS_NONLINEAR);
>>>>    TSSetRHSFunction(ts,NULL,compute_RHS,NULL);
>>>>    TSSetMaxTime(ts,T_FINAL);
>>>>    TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
>>>>    TSSetDM(ts,da);
>>>>    TSSetType(ts,TSCN); //it works with: TSSetType(ts,TSRK);
>>>>    set_IC(da,x);
>>>>    TSSetTimeStep(ts,DT);
>>>>    TSSetSolution(ts,x);
>>>>
>>>>    TSGetSNES(ts,&snes);
>>>>    SNESGetKSP(snes,&ksp);
>>>>    KSPGetPC(ksp,&pc);
>>>>    PCSetType(pc,PCNONE);
>>>>
>>>>    DMSetMatType(da,MATAIJ);
>>>>    DMCreateMatrix(da,&J);
>>>>    ISColoring iscoloring;
>>>>    MatFDColoring  matfdcoloring;
>>>>    DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);
>>>>    MatFDColoringCreate(J,iscoloring,&matfdcoloring);
>>>>
>>>>    MatFDColoringSetType(matfdcoloring,MATMFFD_DS);
>>>>
>>>> // I think I do something wrong in the following 3 lines
>>>>
>>>>    PetscErrorCode (*temp_f)(SNES,Vec,Vec,void*);
>>>>    SNESGetFunction(snes,NULL,&temp_f,NULL);
>>>>    MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))temp_f,NULL);
>>>>
>>>>    MatFDColoringSetUp(J,iscoloring,matfdcoloring);
>>>>
>>>> SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
>>>>    ISColoringDestroy(&iscoloring);
>>>>
>>>>    TSSolve(ts,x);
>>>>
>>>> Thank you,
>>>>
>>>> Oleksandr Koshkarov.
>>>>