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On 07/22/2012 05:28 PM, Jed Brown wrote:
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cite="mid:CAM9tzSnV49u8QUN3AarNZT1i7piMb_XsboDd6_57s74S_UK2sA@mail.gmail.com"
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<div class="gmail_quote">On Sun, Jul 22, 2012 at 10:17 AM, Umut
Tabak <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:u.tabak@tudelft.nl" target="_blank">u.tabak@tudelft.nl</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
Helmholtz equation, 3d discretization of a fluid domain, </blockquote>
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<div>Do you mean indefinite Helmholtz (frequency-domain) or
time-domain (definite)? Sorry, I have to ask...</div>
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<div>What is the wave number? How many grid points per
wavelength?</div>
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Well, basically, I am not interested in time domain response. What I
would like to do is to find the eigenvalues/vectors of the system so
it is in the frequency domain. What I was doing it generally is the
fact that I first factorize the operator matrix with the normal
factorization operation and use it to do multiple solves in my Block
Lanczos eigenvalue solver. Then in my performance evaluations I saw
that this is the point that I should make faster, then I realized
that I could solve this particular system, that is pinned in your
words, faster with iterative methods almost %20 percent faster. And
this is the reason why I am trying to dig under.<br>
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cite="mid:CAM9tzSnV49u8QUN3AarNZT1i7piMb_XsboDd6_57s74S_UK2sA@mail.gmail.com"
type="cite">
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<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">basically
the operator is singular however for my problem I can delete
one of the rows of the matrix, for this case, I and get a
non-singular operator that I can continue my operations,
basically, I am getting a matrix with size n-1, where original
problem size is n.</blockquote>
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<div>This is often bad for iterative solvers. See the User's
Manual section on solving singular systems. What is the
condition number of the original operator minus the zero
eigenvalue (instead of "pinning" on point)?</div>
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This is not clear to me... You mean something like projecting the
original operator on the on the zero eigenvector, some kind of a
deflation.<br>
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