Towards an Exascale Enabled Sparse Solver Repository

Thies, Jonas; Galgon, Martin; Shahzad, Faisal; Alvermann, Andreas; Kreutzer, Moritz; Pieper, Andreas; Röhrig-Zöllner, Melven; Basermann, Achim; Fehske, Holger; Hager, Georg; Lang, Bruno; Wellein, Gerhard

doi:10.1007/978-3-319-40528-5_13

Cited by 6 publications

(14 citation statements)

References 42 publications

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“…In particular the impact of data structures on heterogeneous performance is still underrated in many projects. On top of GHOST we have defined an interface layer that can be used by algorithms and application developers for flexible software development (see [31]).…”

Section: Contributionmentioning

confidence: 99%

“…While other solutions focus on broad applicability, which often comes with sacrificing some performance, achieving optimal efficiency for selected applications without losing sight of possible broader applicability is clearly the main target of GHOST development. Within the ESSEX effort, we supply mechanisms to use GHOST in higher level software frameworks using the PHIST library [31]. To give an example, in [17] we have demonstrated the feasibility and performance gain of using PHIST to leverage GHOST for a Krylov-Schur algorithm as implemented in the Trilinos package Anasazi [3].…”

Section: An Overview Of Ghostmentioning

confidence: 99%

“…Replacing the norm computation (nrm2) and the dot product in Algorithm 1 by a vector addition (axpy) yields the polynomial filter in our ChebFD scheme. For a more detailed description of ChebFD (which is also part of our BEAST-P solver), and the relation to KPM-DOS we refer to the report on the ESSEX solver repository [31] and to [25]. In ChebFD the polynomial filter is [16] applied to a subspace of vectors and also optimization stage 2 (see Algorithm 3) can be applied.…”

Section: Inner Eigenvalue Computation With Chebyshev Filter Diagonalimentioning

confidence: 99%

“…In the algorithms layer various classic, application-specific and novel eigensolvers have been implemented and reformulated in view of the holistic PE process. A comprehensive survey on the activities in the algorithms layer (including FT) is presented in [31]. There we also report on the software engineering process to allow for concurrent development of software in all three layers.…”

Section: Introductionmentioning

confidence: 99%

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Performance Engineering and Energy Efficiency of Building Blocks for Large, Sparse Eigenvalue Computations on Heterogeneous Supercomputers

Kreutzer¹,

Thies

Pieper

et al. 2016

Lecture Notes in Computational Science and Engineering

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Numerous challenges have to be mastered as applications in scientific computing are being developed for post-petascale parallel systems. While ample parallelism is usually available in the numerical problems at hand, the efficient use of supercomputer resources requires not only good scalability but also a verifiably effective use of resources on the core, the processor, and the accelerator level. Furthermore, power dissipation and energy consumption are becoming further optimization targets besides time to solution. Performance Engineering (PE) is the pivotal strategy for developing effective parallel code on all levels of modern architectures. In this paper we report on the development and use of low-level parallel building blocks in the GHOST library ("General, Hybrid, and Optimized Sparse Toolkit"). We demonstrate the use of PE in optimizing a density of states computation using the Kernel Polynomial Method, and show that reduction of runtime and reduction of energy are literally the same goal in this case. We also give a brief overview of the capabilities of GHOST and the applications in which it is being used successfully.

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Section: Contributionmentioning

confidence: 99%

Section: An Overview Of Ghostmentioning

confidence: 99%

Section: Inner Eigenvalue Computation With Chebyshev Filter Diagonalimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance Engineering and Energy Efficiency of Building Blocks for Large, Sparse Eigenvalue Computations on Heterogeneous Supercomputers

Kreutzer¹,

Thies

Pieper

et al. 2016

Lecture Notes in Computational Science and Engineering

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“…Given these needs, the ELPA-AEO and ESSEX-II projects contribute to the development and implementation of efficient highly parallel methods for eigenvalue problems, in different contexts.Both projects are aimed at adding new features (concerning, e.g., performance and resilience) to previously developed methods and at providing additional functionality with new methods. Building on the results of the first ESSEX funding phase [14,34], ESSEX-II again focuses on iterative methods for very large eigenproblems arising, e.g., in quantum physics. ELPA-AEO's main application area is electronic structure computation, and for these moderately sized eigenproblems direct methods are often superior.…”

mentioning

confidence: 99%

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

Alvermann

Basermann

Bungartz

et al. 2019

Japan J. Indust. Appl. Math.

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We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications -Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.Keywords ELPA-AEO · ESSEX · eigensolver · parallel · mixed precision IntroductionEigenvalue computations are at the core of simulations in various application areas, including quantum physics and electronic structure computations. Being able to best utilize the capabilities of current and emerging high-end computing systems is essential for further improving such simulations with respect to space/time resolution or by including additional effects in the models. Given these needs, the ELPA-AEO and ESSEX-II projects contribute to the development and implementation of efficient highly parallel methods for eigenvalue problems, in different contexts.Both projects are aimed at adding new features (concerning, e.g., performance and resilience) to previously developed methods and at providing additional functionality with new methods. Building on the results of the first ESSEX funding phase [14,34], ESSEX-II again focuses on iterative methods for very large eigenproblems arising, e.g., in quantum physics. ELPA-AEO's main application area is electronic structure computation, and for these moderately sized eigenproblems direct methods are often superior. Such methods are available in the widely used ELPA library [19], which had originated in an earlier project [2] and is being improved further and extended with ELPA-AEO.In Sections 2 and 3 we briefly report on the current state and on recent achievement in the two projects, with a focus on aspects that may be of particular interest to prospective users of the software or the underlying methods.Mixed precision in the ELPA-AEO and ESSEX-II projects 3In Section 4 we turn to computations involving different precisions. Looking at three examples from the two projects we describe how lower or higher precision is used to reduce the computing time. The ELPA-AEO projectIn the ELPA-AEO project, chemists, mathematicians and computer scientists from the Max Planck Computing and Data Facility in Garching, the Fritz Haber Institute of the Max Planck Society in Berlin, the Technical University of Munich, and the University of Wuppertal collaborate to provide highly scalable methods for solving moderately-sized (n 10 6 ) Hermitian eigenvalue problems. Such problems arise, e.g., in electronic structure computations, and during the earlier ELPA project, efficient...

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ESSEX: Equipping Sparse Solvers For Exascale

Alappat¹,

Alvermann²,

Basermann³

et al. 2020

Software for Exascale Computing - SPPEXA 2016-2019

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The ESSEX project has investigated programming concepts, data structures, and numerical algorithms for scalable, efficient, and robust sparse eigenvalue solvers on future heterogeneous exascale systems. Starting without the burden of legacy code, a holistic performance engineering process could be deployed across the traditional software layers to identify efficient implementations and guide sustainable software development. At the basic building blocks level, a flexible MPI+X programming approach was implemented together with a new sparse data structure (SELL-C-σ) to support heterogeneous architectures by design. Furthermore, ESSEX focused on hardware-efficient kernels for all relevant architectures and efficient data structures for block vector formulations of the eigensolvers. The algorithm layer addressed standard, generalized, and nonlinear eigenvalue problems and provided some widely usable solver implementations including a block Jacobi-Davidson algorithm, contour-based integration schemes, and filter polynomial approaches. Adding to the highly efficient kernel implementations, algorithmic advances such as adaptive precision, optimized filtering coefficients, and preconditioning have further improved time to solution. These developments

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Towards an Exascale Enabled Sparse Solver Repository

Cited by 6 publications

References 42 publications

Performance Engineering and Energy Efficiency of Building Blocks for Large, Sparse Eigenvalue Computations on Heterogeneous Supercomputers

Performance Engineering and Energy Efficiency of Building Blocks for Large, Sparse Eigenvalue Computations on Heterogeneous Supercomputers

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

ESSEX: Equipping Sparse Solvers For Exascale

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