FEAST—realization of hardware‐oriented numerics for HPC simulations with finite elements

Turek, Stefan; Göddeke, Dominik; Becker, Christian; Buijssen, Sven H. M.; Wobker, Hilmar

doi:10.1002/cpe.1584

Cited by 25 publications

(20 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The test configurations in this paper represent an important building block in our finite element based discretization and solver toolkit FEAST [20], [21], [22]. FEAST is designed to combine high performance computing techniques with state-of-the-art numerical methodology, and executes on large-scale distributed memory machines.…”

Section: The Bigger Picturementioning

confidence: 99%

Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid

Göddeke

Strzodka

2011

IEEE Trans. Parallel Distrib. Syst.

View full text Add to dashboard Cite

Abstract-We have previously suggested mixed precision iterative solvers specifically tailored to the iterative solution of sparse linear equation systems as they typically arise in the finite element discretization of partial differential equations. These schemes have been evaluated for a number of hardware platforms, in particular single precision GPUs as accelerators to the general purpose CPU. This paper reevaluates the situation with new mixed precision solvers that run entirely on the GPU: We demonstrate that mixed precision schemes constitute a significant performance gain over native double precision. Moreover, we present a new implementation of cyclic reduction for the parallel solution of tridiagonal systems and employ this scheme as a line relaxation smoother in our GPU-based multigrid solver. With an alternating direction implicit variant of this advanced smoother we can extend the applicability of the GPU multigrid solvers to very ill-conditioned systems arising from the discretization on anisotropic meshes, that previously had to be solved on the CPU. The resulting mixed precision schemes are always faster than double precision alone, and outperform tuned CPU solvers consistently by almost an order of magnitude.

show abstract

Section: The Bigger Picturementioning

confidence: 99%

Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid

Göddeke

Strzodka

2011

IEEE Trans. Parallel Distrib. Syst.

View full text Add to dashboard Cite

show abstract

“…In previously published work, we demonstrated-for the maximum number of resources available to us at that time-perfect weak scalability for the Poisson problem on up to 320 Xeon processors [9], and excellent strong scaling for applications from linearised elasticity and incompressible flow for an experiment that subsequently quadrupled the resources up to a maximum of 128 CPUs [23].…”

Section: Parallel Multilevel Solversmentioning

confidence: 91%

“…This concept comprises much more than a highly-tuned implementation involving optimal data structures and maximising data reuse to exploit (cache) memory hierarchies. Here, we only illustrate the broad ideas, and refer to previous work for more details [22,23].…”

Section: Hardware-oriented Numericsmentioning

confidence: 99%

See 1 more Smart Citation

GPU acceleration of an unmodified parallel finite element Navier-Stokes solver

Göddeke

Buijssen

Wobker

et al. 2009

2009 International Conference on High Performance Computing &Amp; Simulation

Self Cite

View full text Add to dashboard Cite

We have previously suggested a minimally invasive approach to include hardware accelerators into an existing large-scale parallel finite element PDE solver toolkit, and implemented it into our software FEAST. Our concept has the important advantage that applications built on top of FEAST benefit from the acceleration immediately, without changes to application code. In this paper we explore the limitations of our approach by accelerating a Navier-Stokes solver. This nonlinear saddle point problem is much more involved than our previous tests, and does not exhibit an equally favourable acceleration potential: Not all computational work is concentrated inside the linear solver. Nonetheless, we are able to achieve speedups of more than a factor of two on a small GPU-enhanced cluster. We conclude with a discussion how our concept can be altered to further improve acceleration.

show abstract

“…Many publications are concerned with this approach, we exemplary refer to Keyes and Colella et al, who survey trends towards terascale computing for a wide range of bandwidth-limited applications and conclude that only a combination of techniques from computer architecture, software engineering, numerical modelling and numerical analysis will enable a satisfactory and future-proof scaleout on the application level [6,7]. The FEAST toolkit by Turek et al [8] pursues hardware-oriented numerics for finite-element based discretisations applied to problems from continuum mechanics.…”

Section: Related Workmentioning

confidence: 99%

A simulation suite for Lattice-Boltzmann based real-time CFD applications exploiting multi-level parallelism on modern multi- and many-core architectures

Geveler

Ribbrock

Mallach

et al. 2011

Journal of Computational Science

Self Cite

View full text Add to dashboard Cite

We present a software approach to hardware-oriented numerics which builds upon an augmented, previously published set of open-source libraries facilitating portable code development and optimisation on a wide range of modern computer architectures. In order to maximise efficiency, we exploit all levels of parallelism, including vectorisation within CPU cores, the Cell BE and GPUs, shared memory thread-level parallelism between cores, and parallelism between heterogeneous distributed memory resources in clusters. To evaluate and validate our approach, we implement a collection of modular building blocks for the easy and fast assembly and development of CFD applications based on the shallow water equations: We combine the Lattice-Boltzmann method with fluid-structure interaction techniques in order to achieve real-time simulations targeting interactive virtual environments. Our results demonstrate that recent multi-core CPUs outperform the Cell BE, while GPUs are significantly faster than conventional multi-threaded SSE code. In addition, we verify good scalability properties of our application on small clusters.

show abstract

FEAST—realization of hardware‐oriented numerics for HPC simulations with finite elements

Cited by 25 publications

References 24 publications

Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid

Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid

GPU acceleration of an unmodified parallel finite element Navier-Stokes solver

A simulation suite for Lattice-Boltzmann based real-time CFD applications exploiting multi-level parallelism on modern multi- and many-core architectures

Contact Info

Product

Resources

About