[petsc-users] A flag for FormFunction.
jed at 59A2.org
Thu Jan 14 10:02:22 CST 2010
On Thu, 14 Jan 2010 09:29:33 -0600, Barry Smith <bsmith at mcs.anl.gov> wrote:
> Do you want this so you know when the function is being called
> directly vs when it is being called in computing a Jacobian derivative
> with finite differencing? Do you want the function to do something
> different in the two cases?
Actually, here's a use case where it would be good to know.
Suppose that F does some caching of intermediate quantities needed to
apply J, or that make assembly of J cheaper. For example, I apply
full-accuracy Jacobians unassembled, and assemble something else for
But suppose I wanted to use a preconditioning matrix computed by
coloring, that perhaps also discards some coupling. For example, we
might precondition a 3-component STENCIL_BOX discretization with
STENCIL_STAR where inter-field coupling has been discarded .
Since I have a fast full-accuracy Jacobian, I wouldn't want to use the
inexact thing as the real Jacobian, and caching the intermediate terms
isn't a lot of work, but it might add 20% to the cost of evaluating F(x)
and thus be worthwhile if the line search typically needs less than 5
steps or so. But perhaps more importantly, if I'm recaching J while
computing the preconditioner with FD, then J will be evaluated at
x+eps*y instead of at x which may hurt quadratic convergence.
 STENCIL_STAR preconditioning isn't just hypothetical, I have a nice
2D p-Laplacian example where -snes_mf_operator with STENCIL_STAR
preconditioning beats the analytic (STENCIL_BOX) Jacobian in every
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