OTEGO – Optimization Techniques for Explicit Methods for GPU-Accelerated Solution of Initial Value Problems of Ordinary Differential Equations

Project start: 2016

Funded by:


Project Participants

Project Manager

PD Dr. Matthias Korch

Project Staff

Tim Werner, M.Sc.

Project Description

Graphics processing units (GPUs) are used increasingly to accelerate compute-intensive applications, in particular from the field of scientific computing, through massive parallelism. This project investigates parallel implementations of explicit solution methods for initial value problems (IVPs) of systems of ordinary differential equations (ODEs). Building on the long experience of the working group with these numerical methods on conventional CPU-based parallel computers and preliminary work on the implementation of the basic Euler method on GPUs, the goal of the project is the development of optimization techniques for the efficient and scalable implelementation of explicit solution methods on GPUs. In particular, this includes sophisticated solution methods which offer a higher convergence order than Euler's method and often provide a higher degree of potential parallelism. It will be investigated, how this additional parallelism can be exploited on GPUs. The focal points of the project are the exploitation of specific characteristics of the IVP and the development of self-adaptive solvers that are able to adapt themselves automatically to the IVP to be solved and the architecture of the GPU to be used by selecting an efficient implementation variant and optimized parameters (e.g. block sizes) for this variant automatically.


  • M. Korch and T. Werner.
    An in-depth introduction of multi-workgroup tiling for improving the locality of explicit one-step methods for ODE systems with limited access distance on GPUs.
    Concurrency and Computation: Practice and Experience, e6016.
    Wiley, 2020.
    DOI: 10.1002/cpe.6016
  • M. Korch, P. Raithel and T. Werner.
    Implementation and Optimization of a 1D2V PIC Method for Nonlinear Kinetic Models on GPUs.
    In 2020 28th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP 2020).
    IEEE, 2020.
    DOI: 10.1109/PDP50117.2020.00012
  • M. Korch and T. Werner.
    Multi-Workgroup Tiling to Improve the Locality of Explicit One-Step Methods for ODE Systems with Limited Access Distance on GPUs.
    In Parallel Processingand Applied Mathematics. PPAM 2019, LNCS 12043, pages 3–12.
    Springer, 2020.
    DOI: 10.1007/978-3-030-43229-4_1
  • M. Korch and T. Werner.
    Improving locality of explicit one-step methods on GPUs by tiling across stages and time steps
    Future Generation Computer System. Special Issue on Best of SBAC-PAD 2018, volume 102, pages 889–901.
    Elsevier, 2020.
    DOI: 10.1016/j.future.2019.07.075
  • M. Korch and T. Werner.
    Exploiting Limited Access Distance for Kernel Fusion Across the Stages of Explicit One-Step Methods on GPUs.
    In Proceedings of the 30th International Symposium on Computer Architecture and High Performance Computing (SBAC-PAD 2018), pages 148–157.
    IEEE, 2018.
    DOI: 10.1109/CAHPC.2018.8645892
  • M. Korch and T. Werner.
    Accelerating explicit ODE methods on GPUs by kernel fusion.
    Concurrency and Computation: Practice and Experience, 30:e4470.
    Wiley, 2018.
    DOI: 10.1002/cpe.4470
  • M. Korch, T. Rauber, M. Stachowski and T. Werner.
    Influence of Locality on the Scalability of Method- and System-Parallel Explicit Peer Methods.
    In Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS 2016), 9th Workshop on Computer Aspects of Numerical Algorithms (CANA'16), ACSIS 8, pages 685–694.
    IEEE, 2016.
    CANA best paper award.
    DOI: 10.15439/2016F464

University of Bayreuth -