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<div class="moz-cite-prefix">Dave,<br>
<br>
coupled staggered grid possesses a non-trivial null space. That
means it probably contains not just three translations, three
rotations and a constant pressure. It would be nice if somebody
finally figures out how it looks like. Any ideas? This information
is valuable for building a proper coupled algebraic multigrid
preconditioner.<br>
<br>
As for the fake dofs, I really don't like them. It's perfectly
possible to design a numbering scheme that would only contain real
dofs, and implement it with PETSc. I'm working on it.<br>
<br>
Anton<br>
<br>
On 7/26/13 6:05 PM, Dave May wrote:<br>
</div>
<blockquote
cite="mid:CAJ98EDrcztF+jjDzs+-cEuy0wey174tOZtC1QOOqouGLwQqkrQ@mail.gmail.com"
type="cite">
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charset=ISO-8859-1">
<div dir="ltr">
<div>Yes, the nullspace is important.<br>
</div>
<div>There is definitely a pressure null space of constants
which needs to be considered.<br>
</div>
<div>I don't believe ONLY using<br>
-fieldsplit_1_ksp_constant_null_space<br>
</div>
<div>is not sufficient. <br>
<br>
You need to inform the KSP for the outer syetem (the coupled
u-p system) that there is a null space of constants in the
pressure system. This cannot (as far as I'm aware) be set via
command line args. You need to write a null space removal
function which accepts the complete (u,p) vector which only
modifies the pressure dofs.<br>
<br>
</div>
<div>Take care though when you write this though. Because of the
DMDA formulation you are using, you have introduced
dummy/ficticious pressure dofs on the right/top/front faces of
your mesh. Thus your null space removal function should ignore
those dofs when your define the constant pressure constraint.<br>
<br>
<br>
</div>
<div><br>
Cheers,<br>
</div>
Dave<br>
</div>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">On 26 July 2013 17:42, Matthew Knepley
<span dir="ltr"><<a moz-do-not-send="true"
href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">
<div>
<div class="h5">On Fri, Jul 26, 2013 at 10:13 AM,
Bishesh Khanal <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span>
wrote:<br>
</div>
</div>
<div class="gmail_extra">
<div class="gmail_quote">
<div>
<div class="h5">
<blockquote class="gmail_quote" style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">
On Fri, Jul 26, 2013 at 4:22 PM, Matthew
Knepley <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:knepley@gmail.com"
target="_blank">knepley@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div>
<div>On Fri, Jul 26, 2013 at 9:11
AM, Bishesh Khanal <span
dir="ltr"><<a
moz-do-not-send="true"
href="mailto:bisheshkh@gmail.com"
target="_blank">bisheshkh@gmail.com</a>></span>
wrote:<br>
</div>
</div>
<div class="gmail_extra">
<div class="gmail_quote">
<div>
<div>
<blockquote
class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">
On Fri, Jul 26, 2013
at 2:32 PM, Matthew
Knepley <span
dir="ltr"><<a
moz-do-not-send="true"
href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span>
wrote:<br>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div>On Fri, Jul
26, 2013 at 7:28
AM, Bishesh
Khanal <span
dir="ltr"><<a
moz-do-not-send="true" href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span>
wrote:<br>
</div>
<div
class="gmail_extra">
<div
class="gmail_quote">
<div>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr"><br>
<div
class="gmail_extra"><br>
<br>
<div
class="gmail_quote">
On Wed, Jul
17, 2013 at
9:48 PM, Jed
Brown <span
dir="ltr"><<a
moz-do-not-send="true" href="mailto:jedbrown@mcs.anl.gov"
target="_blank">jedbrown@mcs.anl.gov</a>></span>
wrote:<br>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div>Bishesh
Khanal <<a
moz-do-not-send="true" href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>>
writes:<br>
<br>
> Now, I
implemented
two different
approaches,
each for both
2D and 3D, in<br>
> MATLAB.
It works for
the smaller
sizes but I
have problems
solving it for<br>
> the
problem size I
need (250^3
grid size).<br>
> I use
staggered grid
with p on cell
centers, and
components of
v on cell<br>
> faces.
Similar split
up of K to
cell center
and faces to
account for
the<br>
> variable
viscosity
case)<br>
<br>
</div>
Okay, you're
using a
staggered-grid
finite
difference
discretization
of<br>
variable-viscosity
Stokes. This
is a common
problem and I
recommend<br>
starting with
PCFieldSplit
with Schur
complement
reduction
(make that<br>
work first,
then switch to
block
preconditioner).
</blockquote>
<div><br>
</div>
<div>Ok, I
made my 3D
problem work
with
PCFieldSplit
with Schur
complement
reduction
using the
options:<br>
-pc_fieldsplit_type
schur
-pc_fieldsplit_detect_saddle_point
-fieldsplit_1_ksp_constant_null_space<br>
</div>
<div> <br>
<br>
</div>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">You
can use PCLSC
or<br>
(probably
better for
you), assemble
a
preconditioning
matrix
containing<br>
the inverse
viscosity in
the
pressure-pressure
block. This
diagonal<br>
matrix is a
spectrally
equivalent (or
nearly so,
depending on<br>
discretization)
approximation
of the Schur
complement.
The velocity<br>
block can be
solved with
algebraic
multigrid.
Read the
PCFieldSplit<br>
docs (follow
papers as
appropriate)
and let us
know if you
get stuck.<br>
</blockquote>
</div>
<br>
</div>
<div
class="gmail_extra">Now,
I got a little
confused in
how exactly to
use command
line options
to use
multigrid for
the velocity
bock and PCLS
for the
pressure
block. After
going through
the manual I
tried the
following:<br>
</div>
</div>
</blockquote>
<div> </div>
</div>
<div>You want
Algebraic
Multigrid</div>
<div><br>
</div>
<div>-pc_type
fieldsplit
-pc_fieldsplit_detect_saddle_point</div>
<div>-pc_fieldsplit_type
schur</div>
<div>
-fieldsplit_0_pc_type
gamg</div>
<div>
<div>
-fieldsplit_1_ksp_type
fgmres</div>
<div>
-fieldsplit_1_ksp_constant_null_space</div>
<div>
-fieldsplit_1_ksp_monitor_short</div>
<div>
-fieldsplit_1_pc_type
lsc</div>
<div>-ksp_converged_reason<br>
</div>
<div><br>
</div>
</div>
</div>
</div>
</div>
</blockquote>
<div>I tried the above
set of options but
the solution I get
seem to be not
correct. The
velocity field I get
are quite different
than the one I got
before without using
gamg which were the
expected one.<br>
Note: (Also, I had
to add one extra
option of
-fieldsplit_1_ksp_gmres_restart
100 , because the
fieldsplit_1_ksp
residual norm did
not converge within
default 30
iterations before
restarting).</div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
</div>
</div>
<div>These are all iterative
solvers. You have to make sure
everything converges. </div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>When I set restart to 100, and do
-ksp_monitor, it does converge (for the
fieldsplit_1_ksp). Are you saying that
in spite of having -ksp_converged_reason
in the option and petsc completing the
run with the message "Linear solve
converged due to CONVERGED_RTOL .." not
enough to make sure that everything is
converging ? If that is the case what
should I do for this particular problem
?<br>
</div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
</div>
</div>
<div>If your outer iteration converges, and you do not
like the solution, there are usually two
possibilities:</div>
<div><br>
</div>
<div> 1) Your tolerance is too high, start with it
cranked down all the way (1e-10) and slowly relax it</div>
<div><br>
</div>
<div> 2) You have a null space that you are not
accounting for</div>
<div class="im">
<div><br>
</div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">
<div>I have used the MAC scheme with
indexing as shown in: fig 7.5, page 96
of: <a moz-do-not-send="true"
href="http://books.google.co.uk/books?id=W83gxp165SkC&printsec=frontcover&dq=Introduction+to+Numerical+Geodynamic+Modelling&hl=en&sa=X&ei=v6TmUaP_L4PuOs3agJgE&ved=0CDIQ6AEwAA"
target="_blank">http://books.google.co.uk/books?id=W83gxp165SkC&printsec=frontcover&dq=Introduction+to+Numerical+Geodynamic+Modelling&hl=en&sa=X&ei=v6TmUaP_L4PuOs3agJgE&ved=0CDIQ6AEwAA</a><br>
<br>
Thus I have a DM with 4 dof but there are
several "ghost values" set to 0.<br>
</div>
<div>Would this cause any problem when using
the multigrid ? (This has worked fine when
not using the multigrid.)</div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
</div>
<div>I don't know exactly how you have implemented
this. These should be rows of the identity.</div>
<div class="im">
<div> </div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px
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<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">
<div>I do this problem in the
tutorial with</div>
<div>a constant viscosity.</div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>Which tutorial are you referring to ?
Could you please provide me the link
please ? </div>
</div>
</div>
</div>
</blockquote>
<div><br>
</div>
</div>
<div>
There are a few on the PETSc Tutorials page, but you
can look at this</div>
<div><br>
</div>
<div> <a moz-do-not-send="true"
href="http://www.geodynamics.org/cig/community/workinggroups/short/workshops/cdm2013/presentations/SessionIV_Solvers.pdf"
target="_blank">http://www.geodynamics.org/cig/community/workinggroups/short/workshops/cdm2013/presentations/SessionIV_Solvers.pdf</a></div>
<div><br>
</div>
<div>for a step-by-step example of a saddle-point
problem at the end.</div>
<div><br>
</div>
<div> Matt</div>
<div>
<div class="h5">
<div> </div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote"><br>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">
<div><br>
</div>
<div> Matt</div>
<div>
<div>
<div> </div>
<blockquote
class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div
class="gmail_extra">
<div
class="gmail_quote">
<div>
<div>
</div>
</div>
<div> Matt</div>
<div>
<div>
<div><br>
</div>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div
class="gmail_extra">
<br>
</div>
<div
class="gmail_extra">but
I get the
following
errror:<br>
<br>
[0]PETSC
ERROR:
---------------------
Error Message
------------------------------------<br>
[0]PETSC
ERROR: Null
argument, when
expecting
valid pointer!<br>
[0]PETSC
ERROR: Null
Object:
Parameter # 2!<br>
[0]PETSC
ERROR:
------------------------------------------------------------------------<br>
[0]PETSC
ERROR: Petsc
Release
Version 3.4.2,
Jul, 02, 2013
<br>
[0]PETSC
ERROR: See
docs/changes/index.html
for recent
updates.<br>
[0]PETSC
ERROR: See
docs/faq.html
for hints
about trouble
shooting.<br>
[0]PETSC
ERROR: See
docs/index.html
for manual
pages.<br>
[0]PETSC
ERROR:
------------------------------------------------------------------------<br>
[0]PETSC
ERROR:
src/AdLemMain
on a
arch-linux2-cxx-debug
named edwards
by bkhanal Fri
Jul 26
14:23:40 2013<br>
[0]PETSC
ERROR:
Libraries
linked from
/home/bkhanal/Documents/softwares/petsc-3.4.2/arch-linux2-cxx-debug/lib<br>
[0]PETSC
ERROR:
Configure run
at Fri Jul 19
14:25:01 2013<br>
[0]PETSC
ERROR:
Configure
options
--with-cc=gcc
--with-fc=g77
--with-cxx=g++
--download-f-blas-lapack=1
--download-mpich=1
-with-clanguage=cxx
--download-hypre=1<br>
[0]PETSC
ERROR:
------------------------------------------------------------------------<br>
[0]PETSC
ERROR:
MatPtAP() line
8166 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/mat/interface/matrix.c<br>
[0]PETSC
ERROR:
PCSetUp_MG()
line 628 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/mg/mg.c<br>
[0]PETSC
ERROR:
PCSetUp() line
890 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c<br>
[0]PETSC
ERROR:
KSPSetUp()
line 278 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
[0]PETSC
ERROR:
KSPSolve()
line 399 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
[0]PETSC
ERROR:
PCApply_FieldSplit_Schur()
line 807 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/fieldsplit/fieldsplit.c<br>
[0]PETSC
ERROR:
PCApply() line
442 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c<br>
[0]PETSC
ERROR:
KSP_PCApply()
line 227 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/include/petsc-private/kspimpl.h<br>
[0]PETSC
ERROR:
KSPInitialResidual()
line 64 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itres.c<br>
[0]PETSC
ERROR:
KSPSolve_GMRES()
line 239 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/impls/gmres/gmres.c<br>
[0]PETSC
ERROR:
KSPSolve()
line 441 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
<br>
</div>
<div
class="gmail_extra"><br>
</div>
</div>
</blockquote>
</div>
</div>
</div>
<br>
<br clear="all">
<span><font
color="#888888"><span><font
color="#888888">
<div>
<div><br>
</div>
-- <br>
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>
</font></span></font></span></div>
</div>
<span><font
color="#888888">
</font></span></blockquote>
</div>
<span><font
color="#888888"><br>
</font></span></div>
</div>
<span><font color="#888888">
</font></span></blockquote>
</div>
</div>
</div>
<span><font color="#888888">
<div>
<div><br>
<br clear="all">
<div><br>
</div>
-- <br>
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>
</font></span></div>
</div>
</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
</div>
</div>
</div>
<div>
<div class="h5"><br>
<br clear="all">
<div><br>
</div>
-- <br>
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>
</div>
</div>
</blockquote>
</div>
<br>
</div>
</blockquote>
<br>
</body>
</html>