Fast direct solver for integral equations on massively parallel architectures

Augonnet, Cédric; Pujols, Agnès; Sesques, Muriel

doi:10.1109/usnc-ursi.2015.7303433

Cited by 5 publications

(6 citation statements)

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“…In Reference 33, the IRIS runtime is introduced, which can perform dynamic task partitioning either through user input or automatically via a polyhedral compiler, but no details are provided on how dependencies are handled in this context. Finally, libtask, an advanced runtime system supporting hierarchical tasks in the context of low‐rank linear algebra solvers is presented in Reference 11. This work introduces hierarchical tasks, and dependencies are expressed at the finest level.…”

Section: Related Workmentioning

confidence: 99%

“…While these approaches can be efficient in specific contexts such as dense linear algebra, they suffer from the fact that the task graph is static, making it impossible to select an alternative granularity for a given operation at runtime. For example, when designing linear algebra solvers based on low‐rank approximation algorithms, it is almost impossible to predict the right DAG to ensure good numerical accuracy 8‐12 …”

Section: Introductionmentioning

confidence: 99%

“…For example, when designing linear algebra solvers based on low-rank approximation algorithms, it is almost impossible to predict the right DAG to ensure good numerical accuracy. [8][9][10][11][12] In general, most modern task-based runtime systems suffer from a lack of dynamism in task-graph generation. Some programming models, such as, 7,13,14 support just-in-time DAG submission, but the generation either follows static rules or requires a significant amount of programming effort.…”

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confidence: 99%

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Programming heterogeneous architectures using hierarchical tasks

Faverge

Furmento

Guermouche

et al. 2023

Concurrency and Computation

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SummaryTask‐based systems have become popular due to their ability to utilize the computational power of complex heterogeneous systems. A typical programming model used is the Sequential Task Flow (STF) model, which unfortunately only supports static task graphs. This can result in submission overhead and a static task graph that is not well‐suited for execution on heterogeneous systems. A common approach is to find a balance between the granularity needed for accelerator devices and the granularity required by CPU cores to achieve optimal performance. To address these issues, we have extended the STF model in the StarPU runtime system by introducing the concept of hierarchical tasks. This allows for a more dynamic task graph and, when combined with an automatic data manager, it is possible to adjust granularity at runtime to best match the targeted computing resource. That data manager makes it possible to switch between various data layout without programmer input and allows us to enforce the correctness of the DAG as hierarchical tasks alter it during runtime. Additionally, submission overhead is reduced by using large‐grain hierarchical tasks, as the submission process can now be done in parallel. We have shown that the hierarchical task model is correct and have conducted an early evaluation on shared memory heterogeneous systems using the Chameleon dense linear algebra library.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Programming heterogeneous architectures using hierarchical tasks

Faverge

Furmento

Guermouche

et al. 2023

Concurrency and Computation

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“…Format Algorithm Compute complexity Distributed paradigm Comm. complexity DPLASMA [6] Dense Tile Cholesky 𝑂 (𝑁 3 ) Asynchronous 𝑂 (𝑁 3 ) SLATE [9] Dense Panel Cholesky 𝑂 (𝑁 3 ) Fork-join 𝑂 (𝑁 3 ) LORAPO [7] BLR Tile Cholesky 𝑂 (𝑁 2 ) Asynchronous 𝑂 (𝑁 3 ) H -LU [4] H -matrix H -LU 𝑂 (𝑁𝑙𝑜𝑔(𝑁 )) Asynchronous 𝑂 (𝑁𝑙𝑜𝑔(𝑁 )) STRUMPACK [13] HSS ULV 𝑂 (𝑁 ) Fork-join 𝑂 (𝑁 2 ) Ma et. al.…”

Section: Librarymentioning

confidence: 99%

O(N) distributed direct factorization of structured dense matrices using runtime systems.

Deshmukh,

Yokota,

Bosilca

et al. 2023

Proceedings of the 52nd International Conference on Parallel Processing

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Structured dense matrices result from boundary integral problems in electrostatics and geostatistics, and also Schur complements in sparse preconditioners such as multi-frontal methods. Exploiting the structure of such matrices can reduce the time for dense direct factorization from 𝑂 (𝑁 3 ) to 𝑂 (𝑁 ). The Hierarchically Semi-Separable (HSS) matrix is one such low rank matrix format that can be factorized using a Cholesky-like algorithm called ULV factorization. The HSS-ULV algorithm is highly parallel because it removes the dependency on trailing sub-matrices at each HSS level. However, a key merge step that links two successive HSS levels remains a challenge for efficient parallelization. In this paper, we use an asynchronous runtime system PaRSEC with the HSS-ULV algorithm. We compare our work with STRUMPACK and LORAPO, both state-of-the-art implementations of dense direct low rank factorization, and achieve up to 2x better factorization time for matrices arising from a diverse set of applications on up to 128 nodes of Fugaku for similar or better accuracy for all the problems that we survey. CCS CONCEPTS• Mathematics of computing → Solvers; • Computing methodologies → Massively parallel algorithms; Shared memory algorithms.

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“…Full wave data are simulated with a 3D Maxwell solver [33], based on surface-integral equations in the frequency domain. It can deal with objects made up of dielectric and conducting parts.…”

Section: Unmanned Aerial Vehiclementioning

confidence: 99%

Analysis of SPRITE : A new sparse approach for 3D high resolution RCS imaging

Benoudiba-Campanini

Giovannelli

Massaloux

et al. 2021

IET Radar Sonar & Navi

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Here, the authors present the application of an original high resolution method, named SPRITE (for SParse Radar Imaging TEchnique), for 3D high resolution radar cross section (RCS) imaging. It is based on a regularisation scheme that accounts for information of sparsity and support. The solution is then defined as the minimiser of a penalised and constrained criterion. Optimisation is ensured by an adaptation of the alternating direction method of multipliers that is able to quickly perform calculations using fast Fourier transforms. Through application to synthetic and real data, the authors show that, in comparison to conventional methods, the SPRITE considerably enhances the resolution of the estimated RCS maps leading to a better RCS analysis and control.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Fast direct solver for integral equations on massively parallel architectures

Cited by 5 publications

References 0 publications

Programming heterogeneous architectures using hierarchical tasks

Programming heterogeneous architectures using hierarchical tasks

O(N) distributed direct factorization of structured dense matrices using runtime systems.

Analysis of SPRITE : A new sparse approach for 3D high resolution RCS imaging

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