Program Design Question

[Joshua L. Adelman]

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

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