212	1998	Krister Åhlander	krister@tdb.uu.se	Rapid Development of PDE Solvers

Abstract
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A framework, Compose, for rapid development of  ``PDE solvers'' is presented. 
PDE solvers are programs that solve PDEs (partial differential equations) numerically.
Inheritance hierarchies are used for Compose's key abstractions. Thus, it is
possible to extend the framework with, for instance, new equations or new time
stepping methods.

The implementation of two solvers for the incompressible Navier--Stokes 
equations demonstrates the feasibility of our approach. The second solver 
is an evolvement of the first. This stepwise development illustrates how 
Compose supports the iterative nature of software development. Moreover, 
each equation is developed individually as a component. For each new 
component, the framework encourages a  verification methodology, based 
on a technique of analytical solution forcing.  

Compose solvers are put together by assembling different components. 
Each component, including initial conditions and boundary conditions, 
is visible on the  highest programming level. It is therefore easy  to 
experiment with different solver set-ups just by changing a few 
lines in the main program. A GUI is used to inspect the set-up and to 
change parameters interactively. A Compose solver may be attached with
``monitors'', that can be tailored to control and steer the numerical 
experiment without changing the core of the solver.

The solvers for the incompressible 
Navier--Stokes equations and a solver implemented with a more traditional 
design are compared. We find that the modest overhead of using our high level 
framework is compensated by the following advantages: It is easier to 
extend our solver with new equations; and it is easier to reuse the 
individual pieces in other solvers.