Integrating Multiple Implementations and Structure Exploitation in the Component-Based Design of Parallel ODE Solvers

A COmponent-based Methodology to derive Parallel programs to solve Ordinary Differential Equation (ODE) Solvers, termed COMPODES, is presented. The approach is useful to obtain distributed implementations of numerical algorithms which can be specified by combining linear algebra operations. The main contribution of the approach is the possibility of managing several implementations of the operations and exploiting the problem structure in an elegant and systematic way. As a result, software reusability is enhanced and a clear structuring of the derivation process is achieved. The approach includes a technique to take the lowest level decisions systematically and is illustrated by deriving several implementations of a numerical scheme to solve stiff ODEs.