On Sun, Apr 29, 2018 at 7:44 PM, Oleksandr Koshkarov
<[email protected] <mailto:[email protected]>> wrote:
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)
1) SNESComputeJacobianDefaultColor() creates the Jacobian, fullstop.
2) When you pass J=NULL, the Jacobian is created automatically by DMDA
3) The PC has no influence on the assembly process.
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?
Ignore is the wrong word. How do you form a preconditioner from an
object with no values in it?
Can I still use something like PCSHELL?
What exactly would you do in your shell? If you are only using the
action of an operator, it
usually equivalent to some Krylov method.
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).
The number of dofs does not tell us anything. You would need to know
the sparsity. People regularly solve
problems with billions of unknowns.
Thanks,
Matt
Thank you,
Oleksandr.
On 04/29/2018 05:26 PM, Smith, Barry F. wrote:
On Apr 29, 2018, at 5:40 PM, Oleksandr Koshkarov
<[email protected] <mailto:[email protected]>> 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
<[email protected]
<mailto:[email protected]>> 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.
--
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.caam.rice.edu/%7Emk51/>
