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<div class="moz-cite-prefix">Thanks, Dr. Knepley,<br>
Can I treat AMG and MG like this way. To solve problems with
non-symmetric matrices, MG needs users to provide the coarse mesh
information. This take more complexity on coding than using AMG;
but MG, generally, do better job than MG for non-symmetric
problems. <br>
<br>
Alan<br>
<br>
</div>
<blockquote
cite="mid:CAMYG4G=cwJVbNrGcLHAC30OTWawewqaAqesOnjUSRB7efbdbVw@mail.gmail.com"
type="cite">
<div dir="ltr">On Fri, May 10, 2013 at 8:15 AM, Alan <span
dir="ltr"><<a moz-do-not-send="true"
href="mailto:zhenglun.wei@gmail.com" target="_blank">zhenglun.wei@gmail.com</a>></span>
wrote:<br>
<div class="gmail_extra">
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Thank
you so much, Dr. Brown.<br>
I have a minor question on the 'gamg'. As you said, 'gamg'
works for<br>
many moderately non-symmetric problems. Does this apply
for general<br>
algebraic MG preconditioner or just 'gamg' in PETSc. As
you know, does<br>
'BoomerAMG' suffer from the non-symmetric matrices
problem? Should we<br>
only use regular MG as the preconditioner for highly
non-symmetric problems?<br>
</blockquote>
<div><br>
</div>
<div style="">There is nothing that prevents AMG from
working on non-symmetric matrices (unlike CG),</div>
<div style="">
but there are no guarantees that it will do a good job.</div>
<div style=""><br>
</div>
<div style=""> Matt</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
thanks,<br>
Alan<br>
<br>
> "Zhenglun (Alan) Wei" <<a moz-do-not-send="true"
href="mailto:zhenglun.wei@gmail.com">zhenglun.wei@gmail.com</a>>
writes:<br>
><br>
>> Dear folks,<br>
>> I hope you're having a nice day.<br>
>> For the Poisson solver in
/src/ksp/ksp/example/tutorial/ex45.c, I used<br>
>> the ksp_type = CG to solve it before; it
converges very fast with<br>
>> pc_type = gamg. However, I was trying to check if
the matrix generated<br>
>> by the 'ComputeMatrix' is symmetric by using
"ierr = MatIsSymmetric(B,<br>
>> tol, &flg);". It shows that this matrix is
not exact a symmetric one by<br>
>> setting tol = 0.0. Yet, the matrix is 'symmetric'
if the tol > 0.01.<br>
> The matrix does not enforce boundary conditions
symmetrically.<br>
><br>
>> Does this mean that, even if the matrix is not
exact symmetric, the CG<br>
>> could still be used.<br>
> You happen to be iterating in a "benign" space in
which the operator is SPD.<br>
><br>
>> This brings me a question. Can the CG be used to
solve an actual<br>
>> unsymmetric matrix as long as 'MatIsSymmetric'
returns a 'PETSC_TRUE'<br>
>> value with certain tolerance.<br>
> No.<br>
><br>
>> Is there any rule of thumb for this tolerence?
Also, as a<br>
>> preconditioner, does 'gamg' only work for
symmetric positive-definite<br>
>> matrix? or it works for any matrix or even with
GMRES?<br>
> It works for many moderately non-symmetric, certainly
for something that only<br>
> has non-symmetric boundary conditions.<br>
<br>
</blockquote>
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<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
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