[petsc-users] Using DMDAs with an assigned domain decomposition to Solve Poisson Equation

[Pierpaolo Minelli]

> Il giorno 24 feb 2020, alle ore 12:24, Matthew Knepley <knepley at gmail.com> ha scritto:
> 
> On Mon, Feb 24, 2020 at 5:30 AM Pierpaolo Minelli <pierpaolo.minelli at cnr.it <mailto:pierpaolo.minelli at cnr.it>> wrote:
> Hi,
> I'm developing a 3D code in Fortran to study the space-time evolution of charged particles within a Cartesian domain.
> The domain decomposition has been made by me taking into account symmetry and load balancing reasons related to my specific problem.
> 
> That may be a problem. DMDA can only decompose itself along straight lines through the domain. Is that how your decomposition looks?

My decomposition at the moment is paractically a 2D decomposition because i have:

M = 251 (X)
N = 341 (Y)
P = 161 (Z)

and if i use 24 MPI procs, i divided my domain in a 3D Cartesian Topology with:

m = 4
n = 6
p = 1


>  
> In this first draft, it will remain constant throughout my simulation.
> 
> Is there a way, using DMDAs, to solve Poisson's equation, using the domain decomposition above, obtaining as a result the local solution including its ghost cells values?
> 
> How do you discretize the Poisson equation?

I intend to use a 7 point stencil like that in this example:

https://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/examples/tutorials/ex22f.F90.html <https://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/examples/tutorials/ex22f.F90.html>


> 
>   Thanks,
> 
>     Matt
>  
> As input data at each time-step I know the electric charge density in each local subdomain (RHS), including the ghost cells, even if I don't think they are useful for the calculation of the equation.
> Matrix coefficients (LHS) and boundary conditions are constant during my simulation.
> 
> As an output I would need to know the local electrical potential in each local subdomain, including the values of the ghost cells in each dimension(X,Y,Z).
> 
> Is there an example that I can use in Fortran to solve this kind of problem?
> 
> Thanks in advance
> 
> Pierpaolo Minelli
> 
> 


Thanks
Pierpaolo

> 
> -- 
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
> -- Norbert Wiener
> 
> https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>

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