[petsc-users] Can I use TS routines for operator split formulation

Jed Brown jed at jedbrown.org
Mon Jun 9 16:04:01 CDT 2014

Shriram Srinivasan <shriram at ualberta.ca> writes:
> Au = (k grad(u)_x,  is a discretization of the flux in the x direction, 
> while B is for flux in the y direction. These matrices are assembled by 
> solving local elliptic problems in each cell following a  multiscale 
> finite volume method.
>   To begin, the operator split is done as follows:
> u_t + Au = f ( considering only x dir fluxes) as (u* - u_n)/tau   + A u* 
> = f and solve for u*
> then u_t + B u = f (considering only y dir fluxes) as (u - u*)/tau + B u 
> = f and solve for u at current level.

This is ADI "alternating direction implicit" and tends not to be very
accurate, but more importantly, is a pretty terrible parallel algorithm
that isn't used much any more.  Unless you are implementing this for
nostalgia purposes, I recommend using multigrid (algebraic or geometric)
to solve the coupled problem.  This will be fast and eliminate the
splitting error.
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