[petsc-dev] rename SNES methods ls, tr etc

[Barry Smith]

  So Picard iteration is generally only associated with quasi-linear problems? Or always only associated with quasi-linear problems? Or used all over the place for any kind of problem?


On Dec 3, 2012, at 1:51 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Mon, Dec 3, 2012 at 11:34 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>   What is "a Picard linearization"? As opposed to a non-Picard linearization? Also if you phrase it as in my other email isn't Newton "a Picard linearization"?   You act as if the term "a Picard linearization" has a well defined meaning, but Matt never found it in any book in history.
> 
> If you have a quasi-linear problem, then you can write the homogenous part of the operator as A(u) u. That A(u) is the Picard linearization. Achi calls it the "principle linearization" in some FAS papers because it's provably all that is necessary in the smoother (the other terms in Newton linearization involve lower frequencies, thus are not needed in the smoother).
> 
> Some equations, perhaps most notably the Euler flux, satisfy the "homogeneity property" that F(u) = F'(u) u, i.e., A(u) _is_ the Jacobian, in which case Picard would be equal to Newton. (People don't normally "solve" the flux equation.)