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<div class="moz-cite-prefix">On 21.08.2012 18:32, Matthew Knepley
wrote:<br>
</div>
<blockquote
cite="mid:CAMYG4GnsBQfm_xo4FFMX=n61oanv2G3Sg=zBYu+XJAYMOOfyNA@mail.gmail.com"
type="cite">
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<blockquote class="gmail_quote" style="margin:0 0 0
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<div bgcolor="#FFFFFF" text="#000000"> MUMPS takes only
several minutes and 6 GB of memory to factorize it. <br>
This factorization gives residual on the order of 10e-12 and
solution is indeed correct.<br>
<br>
Nevertheless, you're right, there is numerical null-space in
this matrix since it comes <br>
from the discretization of equation that contains curl curl
operator, but practically this <br>
case is not really the worst one. <br>
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<div>This makes no sense whatsoever. How can you LU factor a
matrix that has a null space?</div>
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</blockquote>
<br>
Matt,<br>
<br>
I'm not sure that I correctly used term numerical null-space in my
post.<br>
The equation is<br>
<br>
curl curl E + kE = -J,<br>
<br>
where k is a function of frequency and conductivity, whenever one of
them becomes small this term gets vanishingly small thus we have
problems since curl curl operator has nontrivial null-space by
definition. So let's say solving this equation for low frequencies
and for models containing air is difficult. <br>
<br>
What kind of magic is inside MUMPS I don't know, but it is able to
handle such cases (e.g. SuperLU and PaStiX fail). <br>
<br>
Also, if it matters, I'm talking about LDLt factorization in MUMPS.<br>
<pre class="moz-signature" cols="72">--
Regards,
Alexander</pre>
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