[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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