Parallel Geometric Multigrid

Hülsemann, Frank; Kowarschik, Markus; Mohr, Marcus; Rüde, Ulrich

doi:10.1007/3-540-31619-1_5

Cited by 48 publications

(32 citation statements)

References 45 publications

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“…Since simulation of a PDE using stencil based methods is a memory-bandwidth intensive procedure, we experiment with partial utilization of nodes. Though an under-utilization of resources, this can find a potential application in solving the coarsest grid on a subset of processes in parallel multilevel methods like geometric multigrid (for example [7], [22]). Our experiments with P = 64 processors and a problem of size 401 3 is shown in Figure 18.…”

Section: Resultsmentioning

confidence: 99%

“…Although stencil codes offer low temporal locality, a future study to modify the model to incorporate its effects looks interesting. Logical future directions are to apply the current work to multilevel methods, such as parallel geometric multigrid [7], [22] and block-structured Adaptive Mesh Refinement (AMR) [23]. This technique can be exploited in parallel geometric multigrid at two levels : (1) at the fine grid level (2) at the coarsest level when using a subset of processes/cores.…”

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confidence: 99%

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A cache-aware approach to domain decomposition for stencil-based codes

Saxena

Jimack

Walkley

2016

2016 International Conference on High Performance Computing &Amp; Simulation (HPCS)

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Abstract-Partial Differential Equations (PDEs) lie at the heart of numerous scientific simulations depicting physical phenomena. The parallelization of such simulations introduces additional performance penalties in the form of local and global synchronization among cooperating processes. Domain decomposition partitions the largest shareable data structures into sub-domains and attempts to achieve perfect load balance and minimal communication. Up to now research efforts to optimize spatial and temporal cache reuse for stencil-based PDE discretizations (e.g. finite difference and finite element) have considered sub-domain operations after the domain decomposition has been determined. We derive a cache-oblivious heuristic that minimizes cache misses at the sub-domain level through a quasi-cache-directed analysis to predict families of high performance domain decompositions in structured 3-D grids. To the best of our knowledge this is the first work to optimize domain decompositions by analyzing cache misses -thus connecting single core parameters (i.e. cache-misses) to true multicore parameters (i.e. domain decomposition). We analyze the trade-offs in decreasing cache-misses through such decompositions and increasing the dynamic bandwidth-per-core. The limitation of our work is that currently, it is applicable only to structured 3-D grids with cuts parallel to the Cartesian Axes. We emphasize and conclude that there is an imperative need to re-think domain decompositions in this constantly evolving multicore era.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

A cache-aware approach to domain decomposition for stencil-based codes

Saxena

Jimack

Walkley

2016

2016 International Conference on High Performance Computing &Amp; Simulation (HPCS)

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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.…”

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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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“…As for many other scientific computing algorithms, the most natural approach to parallelize the lattice Boltzmann method is by domain decomposition, or technically more precise (see [24]) domain partitioning. For domain partitioning, the entire computational domain is divided into several subdomains.…”

Section: Parallelization Of a Simple Full-grid Lbm Codementioning

confidence: 99%

Parallel Lattice Boltzmann Methods for CFD Applications

Körner¹,

Pohl²,

Rüde³

et al.

Lecture Notes in Computational Science and Engineering

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Summary. The lattice Boltzmann method (LBM) has evolved to a promising alternative to the well-established methods based on finite elements/volumes for computational fluid dynamics simulations. Ease of implementation, extensibility, and computational efficiency are the major reasons for LBM's growing field of application and increasing popularity. In this paper we give a brief introduction to the involved theory and equations for LBM, present various techniques to increase the single-CPU performance, outline the parallelization of a standard LBM implementation, and show performance results. In order to demonstrate the straightforward extensibility of LBM, we then focus on an application in material science involving fluid flows with free surfaces. We discuss the required extensions to handle this complex scenario, and the impact on the parallelization technique.

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Parallel Geometric Multigrid

Cited by 48 publications

References 45 publications

A cache-aware approach to domain decomposition for stencil-based codes

A cache-aware approach to domain decomposition for stencil-based codes

ExaStencils: Advanced Stencil-Code Engineering

Parallel Lattice Boltzmann Methods for CFD Applications

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