[petsc-users] 3D multi-dof DMDA and Poisson equation

[Matthew Knepley]

On Wed, Oct 8, 2014 at 3:00 PM, Håkon Strandenes <haakon at hakostra.net>
wrote:

> Hi,
>
> I am making a new, simple incompressible CFD code. I have created a grid
> as a 3D DMDA, with ndof=4, one dof for each velocity component (u,v,w) and
> one for the pressure (p). Currently I am creating a forward Euler step,
> where the velocities are updated based on the velocities and pressure from
> the previous time step. That works great. Now I need to solve a Poisson
> equation for the pressure correction term, enforcing continuity onto my
> solution, and this is where I have a few questions for you:
>
> 1)
> How do I set up my equation system in the most efficient way? The vectors
> from the DMDA is not contiguous in a global sense, i.e. if I map the local
> (i,j,k) indices to a global index with
>
> globId = (info.mx*info.my)*k + (info-.mx)*j + i;
>
> globId is not gontignous on any process. How do I create my coefficient
> matrix, r.h.s. vector and solution vector? Is there some way I can make the
> local parts of the matrix and vectors mimic the decomposition from the
> DMDA? Or should I push all values into a different decomposition scheme,
> where each process holds one contigous slab of the equation system using
> the global ID's calculated above? Have I missed some really basic stuff
> here?
>

See SNES ex5 (which is Poisson when you throw away the extra e^u term).
Hopefully this will explain your question about numbering.


> 2)
> I know that my coefficient matrix from the Poisson equation is symmetric.
> Currently I am still creating and inserting values on both the upper and
> lower diagonal. Is this really necessary? Or is there a "smart" way I can
> save half the storage by only creating the upper or lower part?
>

You can save storage, but not work, so unless you are memory constrained,
this is not worth doing.


> 3)
> I solve a transient problem, but my coefficient matrix is the same for all
> time steps and I only recompute the r.h.s. vector for each time step. I
> have got the impression that KSPsolve "finds out" if the A matrix have
> changed since last invocation or not, recalculating the preconditioner as
> necessary. But still I feel that I should utilize this property more. Do
> you have any tips in how I can use this in the most efficient way possible?
> For example really, really efficient, but expensive, preconditioners?
>

We should figure this out automatically. Please report if this does not
happen for you. Also, we recommend using
TS for timestepping (at least eventually).

 Thanks,

    Matt


> Thanks in advance.
>
> Regards,
> Håkon Strandenes
>



-- 
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
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