Scalabilty Analysis of Parallel Algorithms for the Solution of Systems of Ordinary Differential Equations
Project start: 2000, Project end: 2006
Funded by: DFG
Project ManagerProf. Dr. Thomas Rauber
Prof. Dr. Gudula Rünger, TU Chemnitz
The target of our project is the analysis of existing and the design of new parallel algorithms for the solution of systems of ordinary differential equations and their portable and efficient implementation on modern parallel computers. The analysis does not consider the numerical properties of the underlying methods, but concentrates on the analysis of locality and scalability properties of the resulting parallel algorithms for large numbers of processors.
In doing so, the influence of the three types of parallelism available, data parallelism, task parallelism, and parallelism on the instruction level, and their interactions are to be investigated in particular. Special attention is turned on the investigation of the locality behavior of the solution methods under consideration and their abilities to exploit existing memory hierarchies. Among other things, we are interested in how far an improvement of the scalabilty and locality properties can be obtained by a reordering of the instructions.
As target systems, we consider distributed memory machines as well as machines with a shared main memory. To verify the propositions of the analysis, several variants of the investigated algorithms have to be implemented. On systems with distributed memory, we use MPI, because the group concept of MPI allows for a simple and efficient realization of task parallelism. In implementations for systems with a shared address space, we use a thread library. As programming languages, C and Java are employed.