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<div class="moz-cite-prefix">Randall,<br>
<br>
I can add few more practical notes on EM problem.<br>
<br>
GAMG doesn't work efficiently on curl curl problems because of
mentioned (Jed's message) reasons. One would need to consider
null-space explicitly as in [1] or [2].<br>
Furthermore, even mild grid stretching slows down convergence thus
semi-coarsening is another essential thing to consider. Here you
can find some tests:<br>
<a class="moz-txt-link-freetext" href="http://proceedings.fyper.com/eccomascfd2006/documents/560.pdf">http://proceedings.fyper.com/eccomascfd2006/documents/560.pdf</a><br>
<br>
1. Hiptmair R. 1998. Multigrid method for Maxwell’s equations.
SIAM Journal on Numerical Analysis 36, 204–225<br>
2. Arnold D.N., Falk R.S. and Winther R. 2000. Multigrid in H(div)
and H(curl). Numerische Mathematik 85, 197–217.<br>
<br>
On 15.09.2012 00:18, Jed Brown wrote:<br>
</div>
<blockquote
cite="mid:CAM9tzS=DaCa26PJ1V_h5D=GRv7FkuB5H4c=QSx9wsfgX_5soMQ@mail.gmail.com"
type="cite">
<div class="gmail_quote">On Fri, Sep 14, 2012 at 5:11 PM, Randall
Mackie <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:rlmackie862@gmail.com" target="_blank">rlmackie862@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 id=":62v">If you would be interested, I could dump the
matrix and send it to you to see if you can figure out a
fix.<br>
I have no idea if GAMG would even be a good preconditioner
(this is a ill-conditioned EM</div>
</blockquote>
<div><br>
</div>
<div>This is very important information. What specific EM system
are you solving? Is the shift, positive, negative or complex?
What discretization. What scale do you need to solve and how
performance-sensitive is the application.</div>
<div><br>
</div>
<div>These problems can be huge rabbit holes for multilevel
methods, depending on the parameter range and necessary scale.
Efficient solvers will require extra work since black-box
methods cannot cheaply determine things like the large
curl-curl null space.</div>
<div><br>
</div>
<div>PETSc folks: We should make an example using auxiliary
space preconditioning so that we can have an FAQ on this.</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div id=":62v"> problem), but<br>
I have reasons to believe that MG in general, if done right,
would work. I was hoping to test this<br>
with the GAMG preconditioner, without having to do too much
work on interpolation operators, etc.</div>
</blockquote>
</div>
<br>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Regards,
Alexander</pre>
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