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Related papers: NLSEmagic: Nonlinear Schr\"odinger Equation Multid…

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This paper presents a linear, decoupled, mass- and energy-conserving numerical scheme for the multi-dimensional coupled nonlinear Schr\"odinger (CNLS) system. The scheme combines the fourth-order compact difference approximation in space…

Numerical Analysis · Mathematics 2025-11-18 Ying Gao , Hongfei Fu , Xiaoying Wang

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-20 Utkarsh Utkarsh , Valentin Churavy , Yingbo Ma , Tim Besard , Prakitr Srisuma , Tim Gymnich , Adam R. Gerlach , Alan Edelman , George Barbastathis , Richard D. Braatz , Christopher Rackauckas

Low order, sequential or non-massively parallel finite elements are generaly used for three-dimensional gravity modelling. In this paper, in order to obtain better gravity anomaly solutions in heterogeneous media, we solve the gravimetry…

Numerical Analysis · Mathematics 2021-12-08 Abal-Kassim Cheik Ahamed , Frederic Magoules

Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…

Numerical Analysis · Mathematics 2025-12-23 Manuel Liebchen , Robert Jendersie , Utku Kaya , Christian Lessig , Thomas Richter

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

Computational Engineering, Finance, and Science · Computer Science 2024-01-26 Kasia Świrydowicz , Nicholson Koukpaizan , Maksudul Alam , Shaked Regev , Michael Saunders , Slaven Peleš

We present an open-source CUDA-based package that consists of a compilation of exponential integrators where the action of the matrix exponential or the $\varphi_l$ functions on a vector is approximated using the method of polynomial…

Numerical Analysis · Mathematics 2024-10-23 Pranab J Deka , Alexander Moriggl , Lukas Einkemmer

This paper introduces a second-order method for solving general elliptic partial differential equations (PDEs) on irregular domains using GPU acceleration, based on Ying's kernel-free boundary integral (KFBI) method. The method addresses…

Numerical Analysis · Mathematics 2024-04-24 Liwei Tan , Minsheng Huang , Wenjun Ying

We present a novel, hardware-agnostic implementation strategy for lattice Boltzmann (LB) simulations, which yields massive performance on homogeneous and heterogeneous many-core platforms. Based solely on C++17 Parallel Algorithms, our…

Computational Physics · Physics 2021-05-11 Jonas Latt , Christophe Coreixas , Joël Beny

Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision…

High Energy Physics - Lattice · Physics 2010-12-06 Ronald Babich , Michael A. Clark , Bálint Joó

Heterogeneous systems are becoming more common on High Performance Computing (HPC) systems. Even using tools like CUDA and OpenCL it is a non-trivial task to obtain optimal performance on the GPU. Approaches to simplifying this task include…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-01-11 Marek Blazewicz , Steven R. Brandt , Peter Diener , David M. Koppelman , Krzysztof Kurowski , Frank Löffler , Erik Schnetter , Jian Tao

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is…

Quantum Physics · Physics 2025-11-25 David J. Fernández C. , O. Pavón-Torres

Efficiently exploiting GPUs is increasingly essential in scientific computing, as many current and upcoming supercomputers are built using them. To facilitate this, there are a number of programming approaches, such as CUDA, OpenACC and…

Performance · Computer Science 2017-11-07 G. D. Balogh , I. Z. Reguly , G. R. Mudalige

Recent efforts to improve the performance of neural network (NN) accelerators that meet today's application requirements have given rise to a new trend of logic-based NN inference relying on fixed-function combinational logic (FFCL). This…

Hardware Architecture · Computer Science 2023-04-14 Jingkai Hong , Arash Fayyazi , Amirhossein Esmaili , Mahdi Nazemi , Massoud Pedram

In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…

Cryptography and Security · Computer Science 2014-12-05 Hamza Jeljeli

A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces…

Machine Learning · Computer Science 2025-02-24 Jaron Maene , Vincent Derkinderen , Pedro Zuidberg Dos Martires

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…

Optimization and Control · Mathematics 2025-08-26 Xiyan Hu , Titus Parker , Connor Phillips , Yifa Yu

Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore…

Computational Engineering, Finance, and Science · Computer Science 2026-04-30 Dan Gluck , Yotam Mimran , Andrey Karenskih , Talya Vaknin , Omri Wolf , Ruti Ben-Shlomi , Johannes Gebert

This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…

Computation · Statistics 2015-03-13 Hua Zhou , Kenneth Lange , Marc A. Suchard

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…

Computational Physics · Physics 2020-01-08 Lianhua Zhu , Peng Wang , Songze Chen , Zhaoli Guo , Yonghao Zhang

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…

Computational Engineering, Finance, and Science · Computer Science 2021-05-19 Hao Zhou , Kaushik Bhattacharya