Meta-Tuning in MTL4

Gottschling, Peter; Steinhardt, Cornelius

doi:10.1063/1.3498599

Cited by 8 publications

(8 citation statements)

References 3 publications

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“…For this task we have chosen iterative solvers with standard preconditioners and parameters as listed in Table 7.1. The PFC equation is implemented in the finite element framework AMDiS [66,57] using the linear algebra backend MTL4 [33,22,34] in sequential calculations and PETSc [15] for parallel calculation for the block-preconditioner (4.1) and the inner iterative solvers. As outer solver, a FGMRES method is used with restart parameter 30 and modified Gram-Schmidt orthogonalization procedure.…”

Section: Analysis Of the Pseudospectrum As It Can Be Seen By Simple C...mentioning

confidence: 99%

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Praetorius¹,

Voigt²

2015

SIAM J. Sci. Comput.

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We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and thus offers the opportunity to study long time behaviour of materials with atomic details. This requires adaptive time stepping and efficient time discretization schemes, for which we use an embedded Rosenbrock scheme. To resolve spatial scales of practical relevance, parallel algorithms are also required, which scale to large numbers of processors. The developed preconditioner provides such a tool. It is based on an approximate factorization of the system matrix and can be implemented efficiently. The preconditioner is analyzed in detail and shown to speed up the computation drastically.

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Section: Analysis Of the Pseudospectrum As It Can Be Seen By Simple C...mentioning

confidence: 99%

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Praetorius¹,

Voigt²

2015

SIAM J. Sci. Comput.

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“…For instance, loop unrolling can be parametrized in the function call or by formulas taking the argument type, the computed expression, or the underlying platform into consideration. It has been demonstrated [6] that the generated code has identical performance as its handwritten counter-part.…”

Section: B Abstractions Of Distributed Datamentioning

confidence: 93%

“…Incorporating meta-programming in numeric highperformance software enabled a new kind of tuning, called meta-tuning, that allows for generating tuned executables with every standard C ++ compiler [6]. For instance, loop unrolling can be parametrized in the function call or by formulas taking the argument type, the computed expression, or the underlying platform into consideration.…”

Section: B Abstractions Of Distributed Datamentioning

confidence: 99%

“…• Replace algorithms (like linear solvers) without changing the remainder of the application; • Substitute data structures (like matrix types) with compatible ones without rewriting the calculations; • Benefit from specialized codes (like hand-tuned BLAS routines) without stating it explicitly; • Mix and match orthogonal components leading to an exponential growth of functionality over the size of the library; • Utilize user-defined and third-party types like quaternions, high-precision numbers, or rationals; • Debug graphically like with C arrays [5];…”

Section: Motivationmentioning

confidence: 99%

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Productive Parallel Linear Algebra Programming with Unstructured Topology Adaption

Gottschling¹,

Hoefler

2012

2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (Ccgrid 2012)

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Abstract-Sparse linear algebra is a key component of many scientific computations such as computational fluid dynamics, mechanical engineering or the design of new materials to mention only a few. The discretization of complex geometries in unstructured meshes leads to sparse matrices with irregular patterns. Their distribution in turn results in irregular communication patterns within parallel operations.In this paper, we show how sparse linear algebra can be implemented effortless on distributed memory architectures. We demonstrate how simple it is to incorporate advanced partitioning, network topology mapping, and data migration techniques into parallel HPC programs by establishing novel abstractions.For this purpose, we developed a linear algebra libraryParallel Matrix Template Library 4 -based on generic and meta-programming introducing a new paradigm: meta-tuning. The library establishes its own domain-specific language embedded in C ++ . The simplicity of software development is not paid by lower performance. Moreover, the incorporation of topology mapping demonstrated performance improvements up to 29 %. I. MOTIVATIONMany scientific simulations, such as computational fluid dynamics, mechanical engineering or the design of new materials use computations on unstructured grids as their core method ( §II-A). The operations are expressed as linear algebra (LA) with sparse matrices. These matrices are very often unstructured, that is, the distribution of non-zero values and the data dependencies of typical operations, such as matrixvector multiplication, are irregular.Many large-scale scientific HPC applications can highly benefit from specialized data structures and domain-specific algorithms operating on them. On the other hand, strongly specialized implementations are very expensive to expand for new algorithms and new data structures.The introduction of PETSc [1] in the 90s provided reusable algorithms and data structures for many applications leading to a significant increase of productivity in scientific software development. We aim to raise the productivity further with techniques that did not exist yet at the time PETSc was created.The goal is that the linear algebra library adapts itself to the scientific application instead of applications designed around libraries. Such adaption can be achieved thanks to the expressiveness and efficiency of the template system of C ++ [2] [4]. In this work, we focus on the last two, distributing the unstructured matrices and mapping the resulting communication graph to the network topology. Ideally, these tasks are performed without user assistance leading to convenient libraries that allow developers to program with intuitive abstractions but without sacrificing performance ( §II-B-II-F).Domain-decomposition techniques for structured and unstructured grids have been intensively analyzed and libraries that provide good decompositions are ready for use. In contrast to it, mapping those unstructured grids and their according irregular communication topologies onto sta...

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“…However, this user-friendliness does not harm the performance. To the contrary, advanced meta-programming techniques not only avoid run-time overhead but even enable new forms of performance tuning [36]. The future development will include more specialized solutions for applications like the one in this paper.…”

Section: Pmtl4mentioning

confidence: 99%

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

Anciaux–Sedrakian

Gottschling

Gratien

et al. 2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Re´sume´-Revue des algorithmes de solveurs line´aires utilise´s en simulation de re´servoir, efficaces sur les architectures mate´rielles modernes -Depuis quelques anne´es, en calculs haute performance les constructeurs ont recours de plus en plus a`des architectures base´es sur des unite´s de calculs multicoeurs e´ventuellement acce´le´re´es avec des cartes de type GPGPU (General Purpose Processing on Graphics Processing Units). L'intereˆt de telles architectures offrant un grand nombre d'unite´s de calcul pourrait eˆtre grand pour le domaine de la simulation d'e´coulements multiphasiques en milieu poreux, utilise´e par exemple dans les applications de type se´questration ge´ologique du CO 2 ou simulateur de re´cupe´ration avance´e de pe´trole dans des re´servoirs. Il faut ne´anmoins ve´rifier si les algorithmes des logiciels actuels sont adapte´s pour eˆtre efficaces avec ces nouvelles technologies. La re´solution de grands syste`mes line´aires creux constitue souvent la partie la plus couˆteuse des simulateurs d'e´coulement en milieu poreux. En effet, ces syste`mes sont souvent mal conditionne´s duˆau caracte`re souvent tre`s he´te´roge`ne et anisotrope des donne´es ge´ologiques. Les solveurs line´aires constituent pour ces raisons un point crucial pour les performances de ces simulateurs. Dans cet article, nous proposons un panorama des diffe´rents algorithmes de solveurs line´aires et de pre´conditionneurs utilise´s dans nos applications. Nous analysons leur efficacite´nume´rique et leur performance en fonction de diffe´rentes configurations mate´rielles. Nous proposons une nouvelle approche, base´e sur la programmation hybride, performante sur des architectures he´te´roge`nes a`base de processeurs multicoeurs ou d'acce´le´rateurs de type GPGPU. Cette approche est valide´e dans l'imple´mentation d'un BiCGStab pre´conditionneá vec des algorithmes de type ILU(0), BSSOR, pre´conditionneur polynomial ou CPR-AMG. Des tests de performances ont alors e´te´effectue´s sur differents cas d'e´tudes d'e´coulement en milieu poreux, utilisant des maillages de grande taille.Abstract -Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures -In the past few years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO 2 geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is "are current algorithms and software able to use these new technologies efficiently?" The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPUconsuming part of such simulators. This paper proposes a survey on various solver and preconditioner

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Meta-Tuning in MTL4

Cited by 8 publications

References 3 publications

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Productive Parallel Linear Algebra Programming with Unstructured Topology Adaption

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

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