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Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…

Developing kernels for Processing-In-Memory (PIM) platforms poses unique challenges in data management and parallel programming on limited processing units. Although software development kits (SDKs) for PIM, such as the UPMEM SDK, provide…

Hardware Architecture · Computer Science 2025-10-21 Krystian Chmielewski , Jarosław Ławnicki , Uladzislau Lukyanau , Tadeusz Kobus , Maciej Maciejewski

This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving…

Mathematical Software · Computer Science 2017-11-15 Kasia Świrydowicz , Noel Chalmers , Ali Karakus , Timothy Warburton

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…

Computational Physics · Physics 2024-05-01 Adela Habib , Joshua Finkelstein , Anders M. N. Niklasson

In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on finite mixture estimation. In this framework, we propose a…

Computation · Statistics 2012-01-31 Gilles Celeux , Stéphane Chrétien , Florence Forbes

Deploying mixed-precision neural networks on edge devices is friendly to hardware resources and power consumption. To support fully mixed-precision neural network inference, it is necessary to design flexible hardware accelerators for…

Hardware Architecture · Computer Science 2025-02-04 Liang Zhao , Kunming Shao , Fengshi Tian , Tim Kwang-Ting Cheng , Chi-Ying Tsui , Yi Zou

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…

Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing…

Numerical Analysis · Mathematics 2021-05-04 James Diffenderfer , Daniel Osei-Kuffuor , Harshitha Menon

While many hardware accelerators have recently been proposed to address the inefficiency problem of fully homomorphic encryption (FHE) schemes, none of them is able to deliver optimal performance when facing real-world FHE workloads…

Hardware Architecture · Computer Science 2025-01-31 Junxue Zhang , Xiaodian Cheng , Gang Cao , Meng Dai , Yijun Sun , Han Tian , Dian Shen , Yong Wang , Kai Chen

Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…

Computation · Statistics 2020-05-15 Sharon X. Lee , Geoffrey J. McLachlan , Kaleb L. Leemaqz

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…

Numerical Analysis · Mathematics 2018-05-09 Ludovic Chamoin , Frederic Legoll

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…

Numerical Analysis · Mathematics 2020-12-14 Alec Michael Dunton , Alyson Fox

The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…

Mathematical Software · Computer Science 2013-06-06 Pierre Fortin , Mourad Gouicem , Stef Graillat

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…

Computational Engineering, Finance, and Science · Computer Science 2019-04-30 Eric Neiva , Santiago Badia , Alberto F. Martín , Michele Chiumenti

In this paper, we propose StruM, a novel structured mixed-precision-based deep learning inference method, co-designed with its associated hardware accelerator (DPU), to address the escalating computational and memory demands of deep…

Hardware Architecture · Computer Science 2025-05-20 Michael Wu , Arnab Raha , Deepak A. Mathaikutty , Martin Langhammer , Engin Tunali , Daksha Sharma

In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…

Mathematical Software · Computer Science 2023-06-05 Will Pazner , Tzanio Kolev , Jean-Sylvain Camier

Deep learning has become a useful data analysis method, however mainstream adaption in distributed computer software and embedded devices has been low so far. Often, adding deep learning inference in mainstream applications and devices…

Machine Learning · Computer Science 2022-10-03 Fabian Tschopp

This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. While motivated by the sparse symmetric positive definite (SPD) matrix…

Numerical Analysis · Mathematics 2020-07-15 Stephen F. McCormick , Joseph Benzaken , Rasmus Tamstorf

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…

Computational Physics · Physics 2026-02-18 F. Şık , F. L. Teixeira , B. Shanker

Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…

Programming Languages · Computer Science 2017-07-10 Eva Darulova , Einar Horn , Saksham Sharma