Model-based autotuning of discretization methods in numerical simulations of partial differential equations

Khouzami, Nesrine; Michel, Friedrich; Incardona, Pietro; Castrillón, Jerónimo; Sbalzarini, Ivo F.

doi:10.1016/j.jocs.2021.101489

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…It is the heart of many signal processing and exploring the best algorithmic tool. Examples of their modern applications and usage include image reconstruction in life sciences (Dan et al, 2021;Prigent et al, 2023), visualization of large biological specimens in bioinformatics (Muhlich et al, 2022), weather simulations (Khouzami et al, 2022;Grady et al, 2023), option price prediction in financial mathematics (Alfeus and Schlögl, 2019;Phelan et al, 2019;Salavi et al, 2022), and machine learning (Dao et al, 2019;Aradhya et al, 2022). There are also other applications of FFTW in audio engineering (Faerman et al, 2021(Faerman et al, , 2020.…”

Section: Fftw Software Librarymentioning

confidence: 99%

Parallel computation to bidimensional heat equation using MPI/CUDA and FFTW package

Chakkour

2024

Front. Comput. Sci.

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In this study, we present a fast algorithm for the numerical solution of the heat equation. The heat equation models the heat diffusion over time and through a given region. We engage a finite difference method to solve this equation numerically. The performance of its parallel implementation is considered using Message Passing Interface (MPI), Compute Unified Device Architecture (CUDA), and time schemes, such as Forward Euler (FE) and Runge-Kutta (RK) methods. The originality of this study is research on parallel implementations of the fourth-order Runge-Kutta method (RK4) for sparse matrices on Graphics Processing Unit (GPU) architecture. The supreme proprietary framework for GPU computing is CUDA, provided by NVIDIA. We will show three metrics through this parallelization to compare the computing performance: time-to-solution, speed-up, and performance. The spectral method is investigated by utilizing the FFTW software library, based on the computation of the fast Fourier transforms (FFT) in parallel and distributed memory architectures. Our CUDA-based FFT, named CUFFT, is performed in platforms, which is a highly optimized FFTW implementation. We will give numerical tests to reveal that this method is up-and-coming for solving the heat equation. The final result demonstrates that CUDA has a significant advantage and performance since the computational cost is tiny compared with the MPI implementation. This vital performance gain is also achieved through careful attention of managing memory communication and access.

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Section: Fftw Software Librarymentioning

confidence: 99%

Parallel computation to bidimensional heat equation using MPI/CUDA and FFTW package

Chakkour

2024

Front. Comput. Sci.

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“…Research in automated performance tuning (auto-tuning) can be grouped into two main categories: (1) auto-tuning compiler-generated code optimizations [20], [44], [48], [57], and (2) software auto-tuning [24], [68]. Ashouri et al [2] wrote an excellent survey on machine-learning methods for compiler-based auto-tuning.…”

Section: A Automated Performance Tuningmentioning

confidence: 99%

Benchmarking optimization algorithms for auto-tuning GPU kernels

Schoonhoven,

van Werkhoven,

Batenburg

2022

Preprint

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Recent years have witnessed phenomenal growth in the application, and capabilities of Graphical Processing Units (GPUs) due to their high parallel computation power at relatively low cost. However, writing a computationally efficient GPU program (kernel) is challenging, and generally only certain specific kernel configurations lead to significant increases in performance. Auto-tuning is the process of automatically optimizing software for highly-efficient execution on a target hardware platform. Auto-tuning is particularly useful for GPU programming, as a single kernel requires re-tuning after code changes, for different input data, and for different architectures. However, the discrete, and non-convex nature of the search space creates a challenging optimization problem. In this work, we investigate which algorithm produces the fastest kernels if the time-budget for the tuning task is varied. We conduct a survey by performing experiments on 26 different kernel spaces, from 9 different GPUs, for 16 different evolutionary blackbox optimization algorithms. We then analyze these results and introduce a novel metric based on the PageRank centrality concept as a tool for gaining insight into the difficulty of the optimization problem. We demonstrate that our metric correlates strongly with observed tuning performance.

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“…This infrastructure is being enrich by adding specific purpose computing devices, such as Graphic Processing Units (GPU). Their use is specially useful in external processing architectures where computing intensive tasks of specialized fields such as CAD/CAM [5,35] or Artificial Intelligence (AI) [14] are being offloaded to the Cloud, where the use of GPUs provides better performance [13,32], and allows commodity hardware to perform this operations. This brings superior parallel computing capabilities that tackles new computing intensive needs [34].…”

Section: Introductionmentioning

confidence: 99%

Efficient GPU Cloud architectures for outsourcing high-performance processing to the Cloud

Maciá-Lillo

Ribes²,

Mora³

et al. 2022

Preprint

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The world is becoming increasingly dependant in computing intensive appliances. The appearance of new paradigms such as Internet of Things (IoT), and advances in technologies such as Computer Vision (CV) and Artificial Intelligence (AI) is creating a demand for high performance applications. In this regard, Graphics Processing Units (GPUs) have the ability to provide better performance by allowing a high degree of data parallelism. This devices are also beneficial in specialized fields of manufacturing industry such as CAD/CAM. For all this applications, there is a recent tendency to offload this computations to the Cloud, using a computing offloading Cloud architecture. However, the use of GPUs in the Cloud presents some inefficiencies, where GPU virtualization is still not fully resolved, as our research on what main Cloud providers currently offer in terms of GPU Cloud instances shows. To address this problems, this paper first makes a review of current GPU technologies and programming techniques that increase concurrency, to then propose a Cloud computing outsourcing architecture to make more efficient use of this devices in the Cloud.

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Model-based autotuning of discretization methods in numerical simulations of partial differential equations

Cited by 6 publications

References 16 publications

Parallel computation to bidimensional heat equation using MPI/CUDA and FFTW package

Parallel computation to bidimensional heat equation using MPI/CUDA and FFTW package

Benchmarking optimization algorithms for auto-tuning GPU kernels

Efficient GPU Cloud architectures for outsourcing high-performance processing to the Cloud

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