A Massively Parallel Multigrid Method for Finite Elements

Bergen, B.; Gradl, T.; Rüde, Ulrich; Hülsemann, Frank

doi:10.1109/mcse.2006.102

Cited by 77 publications

(51 citation statements)

References 7 publications

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“…they belong to the few algorithms that qualify as starting point to implement scalable parallel solvers. Thus, multigrid methods are widely used on massively parallel computers, and different parallel implementations are available that scale on current supercomputer architectures [3,21,4,5,14,15]. Multigrid methods involve stencil computations on a hierarchy of very fine to successively coarser grids.…”

Section: Algorithmic Engineeringmentioning

confidence: 99%

ExaStencils: Advanced Stencil-Code Engineering

Lengauer

Apel

Bolten

et al. 2014

Lecture Notes in Computer Science

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Abstract. Project ExaStencils pursues a radically new approach to stencil-code engineering. Present-day stencil codes are implemented in general-purpose programming languages, such as Fortran, C, or Java, or derivates thereof, and harnesses for parallelism, such as OpenMP, OpenCL or MPI. ExaStencils favors a much more domain-specific approach with languages at several layers of abstraction, the most abstract being the mathematical formulation, the most concrete the optimized target code. At every layer, the corresponding language expresses not only computational directives but also domain knowledge of the problem and platform to be leveraged for optimization. This approach will enable a highly automated code generation at all layers and has been demonstrated successfully before in the U.S. projects FFTW and SPIRAL for certain linear transforms. The Challenges of Exascale ComputingThe performance of supercomputers is on the way from petascale to exascale. Software technology for high-performance computing has been struggling to keep up with the advances in computing power, from terascale in 1996 to petascale in 2009 on to exascale, now being only a factor of 30 away and predicted for the end of the present decade. So far, traditional host languages, such as Fortran and C, being equipped with harnesses for parallelism, such as MPI and OpenMP, have taken most of the burden, and they are being developed further with some new abstractions, notably the partitioned global address space (PGAS) memory model [1] [10]. Yet, the sequential host languages remain generalpurpose: Fortran or C or, if object orientation is desired, C ++ or Java.The step from petascale to exascale performance challenges present-day software technology much more than the advances from gigascale to terascale and terascale to petascale have. The reason is the explicit treatment of the massive parallelism inside one node of a high-performance cluster cannot be avoided any longer. That is, the cluster nodes must be manycores with high numbers of cores. The reorientation of the computer market from single cores to multicores and manycores has been observed with concern [29]. In the high-performance market, the situation is somewhat alleviated by the fact that the additional cycles that large numbers of cores provide are actually being yearned for. But, the question of how to exploit them with efficient and robust software remains.While the potential for massive parallelism on and off the chip is the single most serious challenge to exascale software technology, other challenges take on a high priority and are frequently being mentioned, such as power conservation, fault tolerance and heterogeneity of the execution platform [2]. At best, one would strive for performance portability, i.e., the ability to switch the software with ease from one platform, when it is being decommissioned, to the next, while maintaining highest performance. ExaStencils Application Domain: Stencil CodesStencil codes have extremely high significance and value for a good-sized c...

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Section: Algorithmic Engineeringmentioning

confidence: 99%

ExaStencils: Advanced Stencil-Code Engineering

Lengauer

Apel

Bolten

et al. 2014

Lecture Notes in Computer Science

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“…In both cases, operations on coarse grids yield poor parallel efficiency due to relative communication overhead, short loops and vectors, short messages, and kernel call overheads. The Hybrid Hierarchical Grid (HHG) approach described in [40] aims to close the gap between finite element flexibility on unstructured grids and the capabilities of multigrid methods on structured grids. A similar approach with distinction of structured and unstructured data and a generalized multigrid and domain decomposition concept is taken in the FEAST project [41].…”

Section: Application Casesmentioning

confidence: 99%

A survey on hardware‐aware and heterogeneous computing on multicore processors and accelerators

Buchty

Heuveline

Karl

et al. 2011

Concurrency and Computation

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Abstract. The paradigm shift towards multicore technologies is offering a great potential of computational power for scientific and industrial applications. It is, however, posing considerable challenges to software development. This problem is impaired by increasing heterogeneity of hardware platforms on both, processor level, and by adding dedicated accelerators. Performance gains for data-and compute-intensive applications can currently only be achieved by exploiting coarse-and fine-grained parallelism on all system levels, and improved scalability with respect to constantly increasing core counts. A key methodology is hardware-aware computing where in all production steps explicit knowledge of processor, memory, and network details is profitably utilized. In this work we provide a survey on current multicore and accelerator technologies. We outline architectural features and show, how these features are exposed to the programmer and how they can be beneficially utilized in the application-mapping process. In particular, we characterize the discrepancy to conventional parallel platforms with respect to hierarchical memory sub-systems, fine-grained parallelism on several system levels, and chip-and system-level heterogeneity. We motivate the necessity of hardware-aware computing and summarize the challenges arising from high-performance heterogeneous computing. Furthermore, we investigate the interaction of hardware and application characteristics for selected applications in numerical simulation.

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“…In particular, there is a great deal of interest in new petascale FE algorithms. The use of multilevel methods such as hierarchical hybrid grids (Bergen et al 2006) will be essential, since these show close to linear scaling of computational complexity with problem size, and therefore will continue to scale well even for the very large problems that will necessitate the use of petascale computers. A similar development process is underway in the field of SE modelling, where various numerical algorithms that are expected to scale to the next generation of supercomputers have also been proposed (Hamman et al 2007;Taylor et al 2008).…”

Section: Implementation On Petascale Computersmentioning

confidence: 99%

Simulation of cardiac electrophysiology on next-generation high-performance computers

Bordas

Carpentieri²,

Fotia³

et al. 2009

Phil. Trans. R. Soc. A.

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Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility of implementing a parallel SE algorithm based on fully unstructured all-hexahedra meshes is discussed. A major computational task is solution of the large algebraic system resulting from FE or SE discretization. Choice of linear solver and preconditioner has a substantial effect on efficiency. A fully parallel implementation based on dynamic partitioning that accounts for load balance, communication and data movement costs is required. Each of these methods must be implemented on nextgeneration supercomputers in order to realize the necessary speedup. The problems that this may cause, and some of the techniques that are beginning to be developed to overcome these issues, are described.

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A Massively Parallel Multigrid Method for Finite Elements

Cited by 77 publications

References 7 publications

ExaStencils: Advanced Stencil-Code Engineering

ExaStencils: Advanced Stencil-Code Engineering

A survey on hardware‐aware and heterogeneous computing on multicore processors and accelerators

Simulation of cardiac electrophysiology on next-generation high-performance computers

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