Component-based derivation of a parallel stiff ODE solver implemented in a cluster of computers

A component-based methodological approach to derive distributed implementations of parallel ODE solvers is proposed. The proposal is based on the incorporation of explicit constructs for performance polymorphism into a methodology to derive group parallel programs of numerical methods from SPMD modules. These constructs enable the structuring of the derivation process into clearly defined steps, each one associated with a different type of optimization. The approach makes possible to obtain a flexible tuning of a parallel ODE solver for several execution contexts and applications. Following this methodological approach, a relevant parallel numerical scheme for solving stiff ODES has been optimized and implemented on a PC cluster. This numerical scheme is obtained from a Radau IIA Implicit Runge-Kutta method and exhibits a high degree of potential parallelism. Several numerical experiments have been performed by using several test problems with different structural characteristics. These experiments show satisfactory speedup results.