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

[Klaij, Christiaan]

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?

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?

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)?


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