211	1998	Krister Åhlander	krister@tdb.uu.se	Implementing Runge--Kutta schemes for reusability
Abstract
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Four different strategies for implementing Runge--Kutta time stepping
schemes are discussed. Explicit Runge--Kutta, ERK, schemes are
studied, but the results can be generalized to diagonally implicit
Runge--Kutta methods as well. The four different strategies combine
the concepts of forward and reverse communication with and without a
state machine approach. The idea of using state machines is novel.

The different implementation strategies are studied for a model
problem, in a parallel multi-block grid code, and in Compose, a PDE
solving environment, which uses overlapping grids and finite
differences. It is found that the state machine approach does not
degrade performance.

The state machine approach with forward communication is advantageous
in the context of a general PDE solving environment. The reason is
that this approach combines the flexibility of reverse communication
with the simplicity of forward communication, which allows for a high
reusability. The incompressible Navier--Stokes equations are shown as
a case where a state machine ERK component is reusable, whereas a
traditional implementation with forward communication would require
modifications in the ERK implementation.

The conclusion is that the the novel ERK communication strategies are
comparable with respect to performance. The choice of implementation
may therefore be driven by other objectives, such as reusability. In
this respect, the state machine implementation is advantantageous.