<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Sun, Apr 29, 2018 at 8:29 PM, Oleksandr Koshkarov <span dir="ltr"><<a href="mailto:olk548@mail.usask.ca" target="_blank">olk548@mail.usask.ca</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF">
<p>Thank you, it clarifies a lot :)<br>
</p>
<blockquote type="cite">
<div>Ignore is the wrong word. How do you form a preconditioner
from an object with no values in it?</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> Can I still
use something like PCSHELL?<br>
</blockquote>
<div><br>
</div>
<div>What exactly would you do in your shell? If you are only
using the action of an operator, it</div>
<div>usually equivalent to some Krylov method.</div>
</blockquote>
<br>
Yes, I was thinking to use FD matrix free Jacobian and for
preconditioning to use Krylov method to invert the linearized
Jacobian which also would be FD matrix free. Sounds bad? <br></div></blockquote><div><br></div><div>It will not be scalable, unless you are using the Boundary Element Method. PDE operators have condition number that</div><div>grows pretty rapidly with size.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div text="#000000" bgcolor="#FFFFFF">
Well, from your advices I convinced to try constructing actual
Jacobian and use it as Jacobian and matrix from which petsc would
construct preconditioner. <br></div></blockquote><div><br></div><div>Or the first option: Apply J matrix-free for the action in a Krylov method, but build a perhaps simplified operator for preconditioning.</div><div>If there is no obvious simplification, then just build the whole thing.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div text="#000000" bgcolor="#FFFFFF">
p.s. Do I reply to emails correctly? or should I replay to
<a class="m_-6720818516411583507moz-txt-link-abbreviated" href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> only? <br>
<br>
Thank you,<br>
Oleksandr.<br>
<br>
<div class="m_-6720818516411583507moz-cite-prefix">On 04/29/2018 06:03 PM, Matthew Knepley
wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">On Sun, Apr 29, 2018 at 7:44 PM,
Oleksandr Koshkarov <span dir="ltr"><<a href="mailto:olk548@mail.usask.ca" target="_blank">olk548@mail.usask.ca</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Thank
you. A little clarification:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.<br>
</blockquote>
So SNESComputeJacobianDefaultColo<wbr>r will use memory
(construct Jacobian) even if preconditioning is set to
PCNONE and J=NULL? (that is what I saw in my example)<br>
</blockquote>
<div><br>
</div>
<div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">1)
SNESComputeJacobianDefaultColo</span><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"><wbr>r()
creates the Jacobian, fullstop.</span><br>
</div>
<div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"><br>
</span></div>
<div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">2)
When you pass J=NULL, the Jacobian is created
automatically by DMDA</span></div>
<div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"><br>
</span></div>
<div><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:small;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">3)
The PC has no influence on the assembly process.</span></div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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.<br>
</blockquote>
So the following command ignores precoditioning?</blockquote>
<div><br>
</div>
<div>Ignore is the wrong word. How do you form a
preconditioner from an object with no values in it?</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> Can I
still use something like PCSHELL?<br>
</blockquote>
<div><br>
</div>
<div>What exactly would you do in your shell? If you are
only using the action of an operator, it</div>
<div>usually equivalent to some Krylov method.</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
SNESSetJacobian(snes,J,J,MatMF<wbr>FDComputeJacobian,0);<br>
<br>
p.s. for my problems if probably be unrealistic to
construct Jacobian (state size will start from N >
1000^4).<br>
</blockquote>
<div><br>
</div>
<div>The number of dofs does not tell us anything. You would
need to know the sparsity. People regularly solve</div>
<div>problems with billions of unknowns.</div>
<div><br>
</div>
<div> Thanks,</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thank you,<br>
<br>
Oleksandr.<br>
<br>
<br>
On 04/29/2018 05:26 PM, Smith, Barry F. wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On Apr 29, 2018, at 5:40 PM, Oleksandr Koshkarov <<a href="mailto:olk548@mail.usask.ca" target="_blank">olk548@mail.usask.ca</a>>
wrote:<br>
<br>
Dear All,<br>
<br>
sorry for spam because of my poor PETSc knowledge (I
am just starting with this nice framework).<br>
<br>
I think, I figured part of it out. However, I want to
point that src/ts/examples/tutorials/ex15<wbr>.c is
misleading. (or maybe it is a bug?)<br>
<br>
in this example we have<br>
<br>
TSGetSNES(ts,&snes);<br>
MatCreateSNESMF(snes,&Jmf);<br>
SNESSetJacobian(snes,Jmf,J,SNE<wbr>SComputeJacobianDefault,NULL);<br>
<br>
// or this: SNESSetJacobian(snes,Jmf,J,SNE<wbr>SComputeJacobianDefaultColor,0<wbr>);<br>
<br>
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.<br>
</blockquote>
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.<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
To avoid it, I used<br>
<br>
MatCreateSNESMF(snes,&J);<br>
<br>
SNESSetJacobian(snes,J,J,MatMF<wbr>FDComputeJacobian,0);<br>
<br>
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)<br>
</blockquote>
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.<br>
<br>
Barry<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thank you and again sorry for the spam,<br>
Oleksandr.<br>
<br>
On 04/28/2018 07:20 PM, Smith, Barry F. wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
~/Src/petsc/src/ts/examples/tu<wbr>torials<br>
$ grep SNESComputeJacobianDefaultColo<wbr>r *.c<br>
ex10.c: ierr = SNESSetJacobian(snes,A,B,SNESC<wbr>omputeJacobianDefaultColor,0);<wbr>CHKERRQ(ierr);<br>
ex15.c: ierr = SNESSetJacobian(snes,Jmf,J,SNE<wbr>SComputeJacobianDefaultColor,0<wbr>);CHKERRQ(ierr);<br>
ex17.c: ierr = SNESSetJacobian(snes,J,J,SNESC<wbr>omputeJacobianDefaultColor,0);<wbr>CHKERRQ(ierr);<br>
<br>
I don't think you need to explicitly create the
MatFDColoring object.<br>
<br>
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.<br>
<br>
<br>
Barry<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On Apr 28, 2018, at 8:05 PM, Oleksandr Koshkarov
<<a href="mailto:olk548@mail.usask.ca" target="_blank">olk548@mail.usask.ca</a>>
wrote:<br>
<br>
Hello All,<br>
<br>
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).<br>
<br>
Here is my best attempt (what wrong with it?):<br>
<br>
DMDACreate3d(PETSC_COMM_WORLD<wbr>,
DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC,
DM_BOUNDARY_PERIODIC,<br>
DMDA_STENCIL_STAR,<br>
NX, NY, NZ,<br>
PETSC_DECIDE, PETSC_DECIDE,
PETSC_DECIDE,<br>
2*3+NC*NS,<br>
1,<br>
NULL, NULL, NULL, &da);<br>
DMSetUp(da);<br>
DMCreateGlobalVector(da,&x);<br>
TSCreate(PETSC_COMM_WORLD,&ts<wbr>);<br>
TSSetProblemType(ts,TS_NONLIN<wbr>EAR);<br>
TSSetRHSFunction(ts,NULL,comp<wbr>ute_RHS,NULL);<br>
TSSetMaxTime(ts,T_FINAL);<br>
TSSetExactFinalTime(ts,TS_EXA<wbr>CTFINALTIME_STEPOVER);<br>
TSSetDM(ts,da);<br>
TSSetType(ts,TSCN); //it works with:
TSSetType(ts,TSRK);<br>
set_IC(da,x);<br>
TSSetTimeStep(ts,DT);<br>
TSSetSolution(ts,x);<br>
<br>
TSGetSNES(ts,&snes);<br>
SNESGetKSP(snes,&ksp);<br>
KSPGetPC(ksp,&pc);<br>
PCSetType(pc,PCNONE);<br>
<br>
DMSetMatType(da,MATAIJ);<br>
DMCreateMatrix(da,&J);<br>
ISColoring iscoloring;<br>
MatFDColoring matfdcoloring;<br>
DMCreateColoring(da,IS_COLORI<wbr>NG_GLOBAL,&iscoloring);<br>
MatFDColoringCreate(J,iscolor<wbr>ing,&matfdcoloring);<br>
<br>
MatFDColoringSetType(matfdcol<wbr>oring,MATMFFD_DS);<br>
<br>
// I think I do something wrong in the following 3
lines<br>
<br>
PetscErrorCode (*temp_f)(SNES,Vec,Vec,void*);<br>
SNESGetFunction(snes,NULL,&te<wbr>mp_f,NULL);<br>
MatFDColoringSetFunction(matf<wbr>dcoloring,(PetscErrorCode
(*)(void))temp_f,NULL);<br>
<br>
MatFDColoringSetUp(J,iscolori<wbr>ng,matfdcoloring);<br>
<br>
SNESSetJacobian(snes,J,J,SNESC<wbr>omputeJacobianDefaultColor,mat<wbr>fdcoloring);<br>
ISColoringDestroy(&iscoloring<wbr>);<br>
<br>
TSSolve(ts,x);<br>
<br>
Thank you,<br>
<br>
Oleksandr Koshkarov.<br>
<br>
</blockquote>
</blockquote>
</blockquote>
</blockquote>
<br>
</blockquote>
</div>
<br>
<br clear="all"><span class="HOEnZb"><font color="#888888">
<div><br>
</div>
-- <br>
<div class="m_-6720818516411583507gmail_signature" data-smartmail="gmail_signature">
<div dir="ltr">
<div>
<div dir="ltr">
<div>What most experimenters take for granted before
they begin their experiments is infinitely more
interesting than any results to which their
experiments lead.<br>
-- Norbert Wiener</div>
<div><br>
</div>
<div><a href="http://www.caam.rice.edu/%7Emk51/" target="_blank">https://www.cse.buffalo.edu/~<wbr>knepley/</a><br>
</div>
</div>
</div>
</div>
</div>
</font></span></div>
</div>
</blockquote>
<br>
</div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div>
</div></div>