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Similarity between Symmetric Gauss-Seidel and ILU0 smoothing

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Old   December 2, 2017, 08:02
Default Similarity between Symmetric Gauss-Seidel and ILU0 smoothing
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Paolo Lampitella
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Dear all,

in the Fluent manual, more specifically at the end of this page:

https://www.sharcnet.ca/Software/Ans...lar_couple_amg

it is stated that their ILU0 smoother is basically written as their Symmetric Gauss-Seidel one, the only difference being how they compute the diagonal blocks.

Not a linear algebra expert here, but the only reference I found on this is in Saad, Iterative Methods for Sparse Linear Systems, pp. 294, but it seems to me that he also states that this is not possible in general, and only cites the case where the system matrix is penta-diagonal as suitable for this equivalence.

Is anyone aware of additional references on this and/or if the Fluent approach (whose matrix is clearly not pentadiagonal) is actually correct?

Not that implementing ILU0 separately would be such a great deal, but would be great if possible by only working on the diagonal.

Thanks
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Old   December 2, 2017, 08:12
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The book of Saad can be found here:

http://www-users.cs.umn.edu/~saad/It...Book_2ndEd.pdf

but the relative page is 308.
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Old   December 2, 2017, 14:33
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Paolo, maybe you can check the references cited in the book of Peric & Ferziger...
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Old   December 4, 2017, 06:02
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Unfortunately, I had no luck with the book of Ferziger...
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Old   December 4, 2017, 06:18
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Quote:
Originally Posted by sbaffini View Post
Unfortunately, I had no luck with the book of Ferziger...

maybe you should enlarge the field of research...I mean, the "smoother" idea is more related to the multigrid philosophy, maybe the book of Brandt can give you some help
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Old   December 4, 2017, 06:43
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At the moment I'm actually investigating the preconditioning world (where ILU0 seems to have a more prominent role) starting from the review of Benzi on JCP (http://www.cs.ucsb.edu/~gilbert/cs21...condSurvey.pdf) and following the references therein.

However, it seems that the formula used by Fluent is ILU0 applied just to the diagonal of the matrix.
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Old   December 4, 2017, 06:54
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Checked also the references in the SPARSKIT2 of Saad?
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Old   December 4, 2017, 07:09
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Finally found it in here:

http://www.netlib.org/templates/templates.pdf

That version is known as DILU, and now all makes more sense

Thanks
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Old   December 4, 2017, 07:38
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BTW, it is also discussed in the recent book "The Finite Volume Method in Computational Fluid Dynamics" by Moukalled et al.
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Old   December 4, 2017, 08:02
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For the sake of completeness, here it is another good reference:

https://www.google.it/url?sa=t&rct=j...NgWw49Li29Ngqt-
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Old   December 9, 2017, 21:49
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Quote:
Originally Posted by sbaffini View Post
Finally found it in here:

http://www.netlib.org/templates/templates.pdf

That version is known as DILU, and now all makes more sense

Thanks

i wanted to point you to it but had only access to phone where i couldn't log in to make comment.

Anyway here is an additional information might be useful to you, when in parallel, during the construction of DILU diagonal if the off diagonal matrix elements are on another processor then they are ignored. (in Fluent's case)
What it means that adding more and and more processors and performance of Fluent's dilu will go down.
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Old   December 11, 2017, 08:14
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Quote:
Originally Posted by arjun View Post
i wanted to point you to it but had only access to phone where i couldn't log in to make comment.

Anyway here is an additional information might be useful to you, when in parallel, during the construction of DILU diagonal if the off diagonal matrix elements are on another processor then they are ignored. (in Fluent's case)
What it means that adding more and and more processors and performance of Fluent's dilu will go down.
I was indeed hoping for your contribution

But I have a question: is it really necessary to neglect offdiagonal terms related to "cells" on other processors? I mean, they actually are available. Is it a consistency reason (in the sense that they are not within the square block related to a given processor)?

Would the same apply also for ILU0? Or, maybe, would you do the same if you had to use the same reasoning for ILU0?

Thanks
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Old   December 11, 2017, 13:02
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Quote:
Originally Posted by sbaffini View Post
I was indeed hoping for your contribution

But I have a question: is it really necessary to neglect offdiagonal terms related to "cells" on other processors? I mean, they actually are available. Is it a consistency reason (in the sense that they are not within the square block related to a given processor)?

Would the same apply also for ILU0? Or, maybe, would you do the same if you had to use the same reasoning for ILU0?

Thanks

The issue is that ILU0 or DILU factorization loop is serial so what they do is that they run it on each processor disregarding other processors. (as if that processor doesn't know of others).

(The issue is for Aij element of matrix we need also Aji element, this is not available. But if you know that matrix is symmetric then you can add this contribution. You can have such switch in your code).

It is not necessary and there might be a parallel way to do factorization too (i searched but i did not find). But shall be less efficient to construct.
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Old   December 11, 2017, 14:12
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Quote:
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The issue is for Aij element of matrix we need also Aji element, this is not available.
Ok, now I see it... I was only considering Aij with j out of processor (and not Aji). Thanks
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