From: KIRK, BENJAMIN (JSC-EG) (NASA) <benjamin.kirk-1@na...> - 2004-02-09 18:13:53
As I remember it, Hughes, Tezduyar, and others use an element-by-element
matrix-free GMRES approach. In this approach the global matrix is never
formed, and each time a matrix-vector product is needed the element matrix
assembly routine (or a functional equivalent) is called. This is more
memory-efficient but more computationally-expensive that assembling the
global matrix and preconditioning it.
In libMesh the global matrix is assembled, and it may be preconditioned as
you see fit. This is generally better than element-by-element
preconditioning. However, if you want to perform element-by-element
preconditioning you can certainly precondition the element matrix (after you
assemble it in your code) before you insert it into the global matrix.
As for matrix-free, Daniel has expressed an interest in this in the past.
It would require some extensions to the linear solver interface, but that is
Does this help?
[mailto:libmesh-devel-admin@...] On Behalf Of seid mehdi
Sent: Monday, February 09, 2004 12:02 PM
To: libmesh-users@...; libmesh-devel@...
Subject: [Libmesh-devel] element by element preconditioning?
Based on hughes,Tezduyar and others it is possible to
solve Navier-Stokes equations with iterative solvers
by the help of element by element preconditioning.
I am using petsc and currently in Petsc there is not
element by element preconditioning(it is said that
this feature may be added to PETSC3.0).
I want to know that does the libmesh solver support
element by element preconditioning for iterative
solvers or not?
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From: Daniel Dreyer <d.dreyer@tu...> - 2004-02-10 20:48:58
On Mon, 9 Feb 2004, KIRK, BENJAMIN (JSC-EG) (NASA) wrote:
> As for matrix-free, Daniel has expressed an interest in this in the past.
> It would require some extensions to the linear solver interface, but that is
Yep, i was pretty curious about matrix-free... But then i did
some moderately bigger systems, and saw that for our exterior acoustics
thing, matrix-free is not really necessary. Really building the matrix
is not "just doable", but it helps a lot handling the matrix, when
you want some special preconditioners, you may need it explicitly.
So, honestly, matrix-free is off my list... But i am still hoping
to find time for helping in the eigenthingy-regime.
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