Summary

Modeling complex systems can lead to solve large ODEs, and/or DAEs systems to understand the dynamic behavior, eventually stiff, of the solutions. The main difficulties in term of parallel implementation of such systems of equations are the poor granularity of the computations, and the sequential nature of the computing. Previous time steps are required to compute current time step. This last constraint occurs in all the time integrator used in computational fluid dynamics of unsteady problems. From the numerical point of view the development of time domain decomposition methods for stiff ODEs problems allows to focus on the time domain decomposition without perturbation coming from the space decomposition. In other side, the classical advantages of the space decomposition on the granularity are not available. From the computer science point of view, especially, for the grid computing architecture, which is characterized by a large number of processors, the space domain decomposition is limited by the size of the problem and the time decomposition becomes necessary. In another side, the low cost of computing resources on the grid architecture change the concept of efficiency. The number of available processors allows to consider these computational resources to improve the confidence in the solution. One can combine several schemes of different orders and different discretisations to validate and to verify the results. Indeed, from the engineering point of view in the design with ODEs/DAEs, the efficiency of the algorithm is more focus on the saving time in the day to day practice.