Program Design Question

[Barry Smith]

On Mon, 8 May 2006, Joshua L. Adelman wrote:

> I am a new user of PETsc and was hoping that a more experienced member of the 
> group could give me some insight as to what would be the proper formulation 
> of the following problem in PETsc. I am attempting to solve the simple ODE:
> d{rho}/dt = K*rho
>

    Is d{rho}/dt implemented simply as {{rho}^{n+1} - {rho}^{n})/dt or do you
have a mass matrix involved?

> Where K is a large rate matrix that doesn't depend on time within the 
> simulation (i.e K(x)) and rho is a vector of densities. K is usually stiff as 
> it contains terms that reflect both diffusive and chemical transitions, and 
> its entries are sparse.   I am interested in the evolution of the system in 
> time as well as the steady-state behavior. I have already implemented a 
> version of the code in Matlab and am looking to write a PETsc version that 
> can be run in parallel on a cluster. In my matlab code, setting up K is fast 
> and the rate limiting step is actually doing the solve.
>
> Is the appropriate approach using the Backward Euler TS to solve the problem?

    If there is not mass matrix then yes, you want to use that.

> Also it is unclear to me whether I need to employ Distributed Arrays (DA).

  If your ODE comes from discretizing a PDE on a structured (rectangular) grid
in 2 or 3d then the DA may be helpful to organize the partitioning of the 
domain.  But so long as you have a way of computing K in parallel (or computing
it fast sequentially (say in Matlab) and then loading it in in parallel then
you have no reason to us DA.

    Barry

>I 
> can provide more information about the nature of the simulation if necessary 
> if it helps in answering my questions.
>
> Any suggestions/insight would be most appreciated.
>
> Josh
>