Research

Current and previous research projects.

Adaptive mixed-precision schemes based on computable error bounds

  • Project application within the Cluster of Excellence SimTech
  • Start: 11/2017
  • Funding period: until Dec. 31, 2019
  • Funding code: PN 2-24
  • Link: SimTech

Mixed-precision schemes are favourable on all current and future architectures, as they potentially allow to execute the bulk of computations in lower than working precision, resulting in more efficient exploitation of hardware resources both in terms of time-to-solution and energy. They effectively double the working set size in the cache hierarchy, and double the effective memory throughput. However, mixed-precision schemes are currently not widely used, because of the a-priori analysis they require. In this project, we derive, analyse and implement a set of tools towards the automatic selection of the “best mixture” of floating point formats in complex applications for guaranteed accuracy.

Towards a digital human

Providing new possibilities to improve the understanding of the neuromuscular system by switching from small-sized clusters model problems to realistic simulations on HPC clusters

  • Joint application to the "Baden-Württemberg Stiftung gGmbH" together with Oliver Röhrle (Institute of Applied Mechanics), Miriam Mehl (Institute for Parallel and Distributed Systems) und Thomas Ertl (Visualisation Research Centre) at the University of Stuttgart.
  • Start: 11/2016
  • Funding period: 3 years

Having available a realistic digital model of a human would provide in many ways tremendous benefits, e.g. it certainly would constitute a quantum leap in personalised healthcare. This grand vision is shared between many researchers worldwide including the Cluster of Excellence for Simulation Technology (SimTech) at the University of Stuttgart through SimTech’s “Overall Human Model” vision. With this proposal, we want to contribute to this grand vision by developing realistic models of the neuromuscular system. This poses not only significant modelling and computational challenges, but also challenges in visualising the simulation results.

More specifically, we employ HPC to extend existing computational and modelling frameworks, which are currently only running on small-scale clusters, to achieve realistic large-scale, biophysical, multi-scale simulations of skeletal muscle mechanics. The aim is to build up a 3D continuum-mechanical skeletal muscle model that contains a realistic number of muscle fibres (~1,000,000) and is controlled by a model of the central nervous system. To do so, the research proposal unifies model improvements, HPC on large-scale (heterogeneous) hardware architectures, efficient numerical techniques, dynamic load balancing and advanced visualisation techniques. In the sense of the overall grand vision, this model provides the basis for many physiological investigations. Further, extensions to this project are simulations of musculoskeletal systems containing multiple synergistic and antagonistic muscles revealing internal loading conditions.

EXA-DUNE

Flexible PDE Solvers, Numerical Methods and Applications

  • Joint application within the Priority Programme "Software for Exascale Computing" (SPP-1648), together with P. Bastian (Heidelberg), S. Turek (Dortmund), M. Ohlberger und Ch. Engwer (Münster), O. Illisch (Clausthal) and O. Iliev (Kaiserslautern)
  • Start: 01/2016
  • Funding period: 3 years
  • Funding code: GO 1758/2-2
  • Link: http://www.sppexa.de/

In this interdisciplinary project consisting of computer scientists, mathematicians and domain experts from the open source projects DUNE and FEAST we develop, analyse, implement and optimise new numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture.
The DUNE software framework combines flexibility and generality with high efficiency by the use of state-of-the-art programming techniques and interchangeable components conforming to a common interface. Incorporating the hardware-oriented numerical techniques of the FEAST project into these components allows us already during the first funding phase to optimally exploit the performance of heterogeneous architectures with their three-level parallelism (SIMD vectorisation, multithreading, message passing) while at the same time being able to support a variety of different applications from the steadily growing DUNE user community.
In order to cope with the increased probability of hardware failures, a central aim in the second funding period is to add flexible, application-orientied resilience capabilities into the framework which, based on a common infrastructure, includes on the one hand ready-to-use self-stabilising iterative solvers and on the other hand global and local checkpoint restart techniques. Continuous improvement of the underlying hardware-oriented numerical methods is achieved by combining matrix-free sum-factorisation based high-order discontinuous Galerkin discretisations with matrix-based algebraic multigrid low-order subspace correction schemes resulting in both robust and performant solvers. On top of that, extreme scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we now focus on the adaptive choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm.
As an integral part of the project we propose to bring together our scalable PDE solver components in a next-generation land-surface model including subsurface flow, vegetation, evaporation and surface runoff. This development is carried out in close cooperation with the Helmholtz-Centre for environmental research (UFZ) in Halle which provides the additional modelling expertise as well as measurement data from multiple sources (experimental sites, geophysical data, remote sensing, ...). Together we set out to provide the environmental research community with an open source tool that contributes to the solution of problems with high social relevance.

Completed projects

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  • Project application within the Cluster of Excellence SimTech
  • Start: 11/2015
  • Funding period: 3 years up to Oct. 31, 2017
  • Funding code: PN2-17

As the hardware at the bottom of the simulation pipeline becomes increasingly fine-grained parallel and heterogeneous, a multitude of portability, performance and usability challenges arise. Several of these will be addressed in this project. The overall intention is to develop efficient numerical methodology, data structures and implementation techniques that enable better future-proof exploitation of the underlying hardware for adaptive problems. We will mainly focus on aspects arising in finite element modelling on GPUs as current example hardware, without neglecting the general applicability of the developed techniques: As the implementation will be done in the DUNE software framework, these “low-level” improvements will be available for a wide range of applications, within and beyond the SimTech Cluster of Excellence.

  • Joint application in cooperation with S. Turek (TU Dortmund)
  • Start: 08/2013
  • Funding period: 3 years
  • Funding code: GO 1758/3-1

This joint project examines numerical methods for massively-parallel multigrid methods for finite element discretisations of variable order. Special emphasis is placed on techniques that enable robustness and uniform scalability on modern heterogeneous hardware architectures, in particular on hybrid systems comprising conventional CPU-like processors combined with throughput-optimised accelerator designs like graphics processors (GPUs). The goal of uniform scalability is very challenging and embraces aspects of numerical scalability (convergence rates independent of problem size and problem partitioning), the minimisation or even avoidance of sequential components on all parallelism layers of hybrid systems, the equal degree of utilisation of all compute resources, and the numerically stable and robust asynchronous and fault-tolerant parallel execution. In addition, novel numerical methods along with suitable implementation techniques are developed and analysed (hardware-oriented numerics), so that efficient -- simultaneously wrt. numerics, parallelism and hardware - discretisation and solution techniques can be provided for a broad range of flow problems. Joint work in this research project is incorporated both in independently usable libraries as well as the common FEAST software package that has been developed intensively during the last years, so that a numerically robust, scalable and recursively configurable methodology for massively-parallel multigrid methods on heterogeneous hardware platforms can be realised and analysed.

  • Joint application within the Priority Programme "Software for Exascale Computing" (SPP-1648), together with P. Bastian and O. Ippisch (Heidelberg), S. Turek (Dortmund), M. Ohlberger und Ch. Engwer (Münster) and O. Iliev (Kaiserslautern)
  • Start: 01/2013
  • Funding period: 3 years
  • Funding code: GO 1758/2-1
  • Link: http://www.sppexa.de/

The aim of this interdisciplinary project, bringing together experts from the open source projects DUNE and FEAST, is to develop, analyse and realise new numerical, algorithmic and computational techniques to enable exascale computing for partial differential equations (PDEs) on heterogeneous massively parallel architectures. As the life time of PDE software is typically much longer than for hardware, flexible but nevertheless hardware-specific software components are developed based on the DUNE platform, which uses state-of-the-art programming techniques to achieve great flexibility and high efficiency to the advantage of a steadily growing user-community. Hardware-oriented numerical techniques of the FEAST project are integrated to optimally exploit the performance of the local (heterogeneous) nodes (multi-core multi-purpose CPUs, special purpose acceleration units like GPUs, etc.), w.r.t. specific structures of the given PDEs. The introduction of a hardware abstraction layer will make it possible to perform the necessary hardware-specific changes of essential components at compile time with at most minimal changes of the application code. Further adding to the great benefits from a combination of the strengths of DUNE and FEAST, modern numerical discretisation’s and solver approaches like adaptive multi-grid, localised spectral methods (e.g. higher-order Discontinuous Galerkin schemes) and a hybrid parallel grid will increase the scalability. The EXA-DUNE toolbox is extended from petascale towards exascale level computing by introducing multi-level Monte Carlo methods for uncertainty quantification and multi-scale techniques which both add an additional layer of coarse grained parallelism, as they require the solution of many weakly coupled problems. The new methodologies and software concepts are applied to flow and transport processes in porous media (fuel cells, CO2 sequestration, large scale water transport), which are grand challenge problems of high relevance to society.

  • Individual proposal for a kick-off funding within the 2nd announcement of the Mercator Research Center Ruhr (MERCUR)
  • Start: 06/2013
  • Funding period: 1 year
  • Funding code: An-2013-0019

Modern computer systems are increasingly heterogeneous, parallel, dynamic and unreliable. To efficiently exploit their potential performance, the underlying numerical and algorithmic methodology has to be explicitly adapted and extended. The scope of this project is the numerical simulation of partial differential equations, in particular the combination of finite element methods with hierarchical multigrid methods. Components of this type often dominate compute times in modern, fast and accurate simulation schemes for application problems, e.g., in continuum mechanics. While in the past few years significant progress has been achieved in terms of uniform scalability, fine-granular parallelisation (GPUs) and runtime efficiency, we now tackle the even more complex challenges of fault tolerance, asynchronicity and communication avoiding: Resilience in case of partial hardware faults will be integrated directly in more robust numerical schemes, and the dramatically increasing disparity between raw floating point performance and data transfers between heterogeneous memory hierarchies mandates substantial research efforts to develop solution methods that are flexible and highly efficient simultaneously. All implementations are integrated into open-source software and are thus widely available for application codes.

  • Individual proposal within the "CUDA Teaching Program", NVIDIA Research
  • Start: 07/2012
  • Funding period: 1 year
  • Funding code: n/a
Dieses Bild zeigt Göddeke
Prof. Dr. rer. nat.

Dominik Göddeke

Head of Institute and Head of Group