OpenSBLI: A framework for the automated derivation and parallel execution of finite difference solvers on a range of computer architectures

Jacobs, Christian T.; Jammy, Satya P.; Sandham, Neil D.

doi:10.1016/j.jocs.2016.11.001

Cited by 55 publications

(58 citation statements)

References 38 publications

(51 reference statements)

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“…To facilitate these investigations, the capabilities of the recently developed OpenSBLI framework [12] are extended to easily generate algorithms with varying amounts of computational and memory intensity. OpenSBLI is a framework for the automated derivation and parallel execution of finite difference-based models.…”

Section: Introductionmentioning

confidence: 99%

Performance evaluation of explicit finite difference algorithms with varying amounts of computational and memory intensity

Jammy

Jacobs

Sandham

2019

Journal of Computational Science

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Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by varying degrees of memory and computational intensity, are evaluated in the context of finite difference methods for fluid dynamics problems. It is shown that, by storing some of the evaluated derivatives as single thread-or process-local variables in memory, or recomputing the derivatives on-the-fly, a speed-up of ∼2 can be obtained compared to traditional algorithms that store all derivatives in global arrays.

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Section: Introductionmentioning

confidence: 99%

Performance evaluation of explicit finite difference algorithms with varying amounts of computational and memory intensity

Jammy

Jacobs

Sandham

2019

Journal of Computational Science

Self Cite

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“…In this paper two methods are used for this purpose: the Finite Element Method (FEM); and the Finite Volume Method (FVM). The Finite Difference Method (FDM) may also be used to solve the RANS equations [14] however this type of analysis is not explored in this paper. A third method of solving for the conservation of mass, momentum and energy is based on a different formulation than that of continuum mechanics, namely the Lattice Boltzmann Method (LBM), the details of which are given in Section 2.2.…”

Section: Continuum Mechanicsmentioning

confidence: 99%

Three computational methods for analysing thermal airflow distributions in the cooling of data centres

Boer

Johns

Delbosc³

et al. 2018

HFF

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This paper uses three different numerical simulation technologies to analyse the thermal airflow distribution in a simple example data center layout. The numerical approaches used are based on finite element, finite volume and lattice Boltzmann methods and are respectively implemented via commercial Multiphysics software, opensource CFD code and GPU based code developed by the authors. Each method includes an appropriate turbulence model and the simulation results focus on comparison of the three methods when applied to 2 rows of datacom racks with cool air supplied by a computer room air conditioner and distributed via an underfloor plenum. Good quantitative agreement between the three methods is seen in terms of the inlet temperatures to the Datacom equipment.Key Words: Data center cooling, Lattice Boltzmann, Finite Element, Finite Volume. IntroductionData centers are facilities hosting information and communications technology (ICT) infrastructure, usually laid out in rows of 2m tall racks. Their operation provides digital services across a range of sectors. The quantity and density of these ICT systems results in a distributed and complex dynamic generation of heat throughout the facility that needs to be transported away from the ICT, referred to as datacom, equipment. This is usually achieved by air cooling, where the heat is transferred and ultimately rejected to the outside environment. The growth of these facilities has been considerable, with data centers consuming only 0.12% of US energy consumption for the year 2000 [1] and that figure having risen to over 2% only ten years later, in 2010 [2]. Globally this figure is currently closer to 1.5%, at a growth of roughly 11% per year over the last decade [3], and approximately 45% of this energy is used in the removal of heat [4]. Improvements to the energy efficiency of these facilities are rapidly becoming paramount, due to the need to reduce both running costs and environmental impact [5].

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“…Multiple DSLs to express stencil-like algorithms have also emerged over time, including Henretty et al (2013); Zhang and Mueller (2012); Christen et al (2011); Unat et al (2011); Köster et al (2014); Membarth et al (2012); Osuna et al (2014); Tang et al (2011); Bondhugula et al (2008); Yount (2015). Other stencil DSLs have been developed with the objective of solving PDEs using finite differences Hawick and Playne (2013), Arbona et al (2017) and Jacobs et al (2016). However, in all cases their use in seismic imaging problems (or even more broadly in science and engineering) has been limited by a number of factors other than technology inertia.…”

Section: Introductionmentioning

confidence: 99%

Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

Louboutin¹,

Lange²,

Luporini³

et al. 2018

Preprint

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We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform Inversion and Reverse-Time Migration are used to invert terabytes of seismic data to create images of the earth's subsurface. Even using modern supercomputers, it can take weeks to process a single seismic survey and create a useful subsurface image. The computational cost is dominated by the numerical solution of wave equations and their corresponding adjoints. Therefore, a great deal of effort is invested in aggressively optimizing the performance of these wave-equation propagators for different computer architectures. Additionally, the actual set of partial differential equations being solved and their numerical discretization is under constant innovation as increasingly realistic representations of the physics are developed, further ratcheting up the cost of practical solvers. By embedding a domain-specific language within Python and making heavy use of SymPy, a symbolic mathematics library, we make it possible to develop finite difference simulators quickly using a syntax that strongly resembles the mathematics. The Devito compiler reads this code and applies a wide range of analysis to generate highly optimized and parallel code. This approach can reduce the development time of a verified and optimized solver from months to days. arXiv:1808.01995v1 [cs.DM] 6 Aug 2018 maintained or extended. In contrast, the use of high-level abstractions and symbolic reasoning provided by domain-specific languages (DSL) can significantly reduce the time it takes to implement and verify individual operators for use in inversion frameworks, as has already been shown for the finite element method (Logg et al., 2012;Rathgeber et al., 2015;Farrell et al., 2013).State-of-the-art seismic imaging is primarily based upon explicit finite difference schemes due to their relative simplicity and ease of implementation (Virieux, 1986;Symes, 2015a;Weiss and Shragge, 2013). When considering how to design a DSL for explicit finite difference schemes, it is useful to recognize the algorithm as being primarily a sub-class of stencil algorithms or polyhedral computation (Henretty et al., 2013; Andreolli et al., 2015;Yount, 2015). However, stencil compilers lack two significant features required to develop a DSL for finite differences: symbolic computational support required to express finite difference discretizations at a high level, enabling these expressions to be composed and manipulated algorithmically; support for algorithms that are not stencil-like, such as source and receiver terms that are both sparse and unaligned with the finite difference grid. Therefore, the design aims behind the Devito DSL can be summarized as:create a high-level mathematical abstraction for programming finite differences to enable composability and algorithmic optimization, insofar as possible use existing compiler technologies to o...

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OpenSBLI: A framework for the automated derivation and parallel execution of finite difference solvers on a range of computer architectures

Cited by 55 publications

References 38 publications

Performance evaluation of explicit finite difference algorithms with varying amounts of computational and memory intensity

Performance evaluation of explicit finite difference algorithms with varying amounts of computational and memory intensity

Three computational methods for analysing thermal airflow distributions in the cooling of data centres

Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

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