[petsc-users] function name and meaning of -pc_fieldsplit_schur_factorization_type

[Matthew Knepley]

On Fri, Mar 16, 2012 at 8:40 AM, Klaij, Christiaan <C.Klaij at marin.nl> wrote:

> The manual page 87 states that "there are several variants
> of the Schur complement preconditioner obtained by dropping some
> of the terms, these can be obtained with
> -pc_fieldsplit_schur_factorization_type <diag,lower,upper,full>"
>
> 1) What is (will be) the name of the corresponding function?
>

There isn't one.


> 2) It would be nice to know what exactly is being dropped. <full>
> is obvious and apparently <diag> drops the right most matrix, but
> what do lower and upper drop?
>

http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/PC/PCFIELDSPLIT.html


> 3) I'm confused about the minus sign in the <diag> form and its
> motivation. It doesn't come from the factorization. Is the rhs
> multiplied with a minus sign as well? Why not follow the sign
> convention of Elman's taxonomy (eq 3 and 4, JCP 227, 2008)?
>

It makes the PC positive definite.

  Matt


>
> dr. ir. Christiaan Klaij
> CFD Researcher
> Research & Development
> E mailto:C.Klaij at marin.nl
> T +31 317 49 33 44
>
> MARIN
> 2, Haagsteeg, P.O. Box 28, 6700 AA Wageningen, The Netherlands
> T +31 317 49 39 11, F +31 317 49 32 45, I www.marin.nl
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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