[petsc-users] Does Petsc have any feature to handle the mirror points?

[Jed Brown]

I assume you are using DA. One way is to use a periodic stencil so that the
local vector has room for those points. Another is to never put them into an
array (you don't really want them in the global system anyway, and the
Jacobian still needs to differentiate through the process by which you
decide what to put in those slots).

For something more complicated like immersed boundary methods, you will
leave those points in and it might be impractical to differentiate through
the computation of values at mirror points. The approximation you use will
then affect convergence rate.

Jed

On Aug 10, 2010 9:42 AM, "Li, Zhisong (lizs)" <lizs at mail.uc.edu> wrote:

  Hi, Petsc Team,

In finite difference computations, we often utilize schemes of five or more
points stencil in one direction. To calculate the interior point next to the
boundary, we need to assume one point out of the domain by extrapolation
(such as a mirror point). As we are required to include all interior points
and boundary points in the system matrix, does Petsc have any feature to
handle these mirror points ? In assembling the matrix for a 3D system of
multiple variables and equations, besides setting up the boundary
conditions, I think this will cost lots of extra effort to specially manage
the points next to the boundary, if Petsc doesn't have any easy way to do
this.

Thank you.


Zhisong Li
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