Parallel Solution of Systems of Ordinary Differential Equations by Adaptive Techniques

Project start: 2010

Funded by: DFG

Project Participants

Project Manager

Prof. Dr. Thomas Rauber, PD Dr. Matthias Korch

Contact Person

PD Dr. Matthias Korch

Project Staff

Dr. Natalia Kalinnik

Dr. Carsten Scholtes

External Partners

Prof. Dr. Gudula Rünger, TU Chemnitz

Project Description

The goal of this project is the development of adaptive parallel algorithms for the efficient solution of initial value problems of systems of ordinary differential equations on modern computer systems and computer systems expected in the near future. The  particular challenge posed by these computer systems is the increasing degree of heterogeneity caused by, for example, heterogeneously and maybe asynchronously working processor cores, deep memory hierarchies and hierarchical interconnection networks. New parallel algorithms are to be developed starting from the existing degree of instruction, task and data parallelism and the memory access behavior of existing sequential solution methods. The approach followed consists of the target-oriented combination of different types of parallelism in connection with the use of specialized adaptive load balancing methods, adaptable data structures and self-adaptive techniques for the optimization of program parameters and the computational structure as well as the memory access behavior. Thus, an efficient dynamic assignment of computations to the heterogeneous resources of the computer system and a better scalability for large parallel computer systems shall be achieved. The adaptive algorithms and data structures will be suited to the time-step-oriented computational structure of solution methods for ordinary differential equations. The numerical properties of the solution methods will not be changed.


Collection of Implementations of Embedded Runge-Kutta Solvers (August 2010)


This collection contains different sequential and parallel implementations of embedded Runge-Kutta solvers which aim at improved locality of memory references and improved scalability for the solution of systems of ordinary differential equations with limited access distance. In particular, the collection contains implementations which require only little more than O(2n) storage space for the solution of a system of ordinary differential equations of size n, but still provide efficient stepsize control.

The implementations and their runtime behavior are described and discussed in detail in the articles

  • Matthias Korch and Thomas Rauber. Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance. Bayreuth Reports on Parallel and Distributed Systems, No. 1, University of Bayreuth, July 2010. URL:, URN: urn:nbn:de:bvb:703-opus-7136
  • Matthias Korch and Thomas Rauber. Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance. To appear in: International Journal of High Performance Computing Applications. SAGE Publications.

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