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Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…

Numerical Analysis · Mathematics 2021-09-14 Sebastián J. Ferraro , David Martín de Diego , Rodrigo T. Sato Martín de Almagro

We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-19 Jinghai He , Haoyu Liu , Yuhang Wu , Zeyu Zheng , Tingyu Zhu

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of…

Numerical Analysis · Mathematics 2015-01-22 Siegfried Cools , Pieter Ghysels , Wim van Aarle , J. Sijbers , Wim Vanroose

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the…

Mathematical Software · Computer Science 2020-09-28 José I. Aliaga , Hartwig Anzt , Thomas Grützmacher , Enrique S. Quintana-Ortí , Andrés E. Tomás

Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…

Numerical Analysis · Mathematics 2026-03-24 Nicolas L. Guidotti , Per-Gunnar Martinsson , Juan A. Acebrón , José Monteiro

We present a highly general implementation of fast multipole methods on graphics processing units (GPUs). Our two-dimensional double precision code features an asymmetric type of adaptive space discretization leading to a particularly…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-02-22 Anders Goude , Stefan Engblom

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…

Interior point methods are widely used for different types of mathematical optimization problems. Many implementations of interior point methods in use today rely on direct linear solvers to solve systems of equations in each iteration. The…

Optimization and Control · Mathematics 2024-02-27 Felix Liu , Albin Fredriksson , Stefano Markidis

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Optimization and Control · Mathematics 2023-05-05 Bharat Kumar , Deepmala , A. K. Das

Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Recently Frommer et al. presented a block Krylov framework that…

Numerical Analysis · Mathematics 2019-12-30 Nils-Arne Dreier , Christian Engwer

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Numerical Analysis · Mathematics 2021-05-18 Jennifer A. Loe , Christian A. Glusa , Ichitaro Yamazaki , Erik G. Boman , Sivasankaran Rajamanickam

Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…

Hardware Architecture · Computer Science 2022-01-20 Francesco Sgherzi , Alberto Parravicini , Marco Domenico Santambrogio

Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…

Numerical Analysis · Mathematics 2024-12-24 Tomonori Kouya

Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…

Mathematical Software · Computer Science 2015-06-15 Jan Verschelde , Xiangcheng Yu

A finite-difference Micromagnetic simulation code written in MATLAB is presented with Graphics Processing Unit (GPU) acceleration. The high performance of Graphics Processing Unit (GPU) is demonstrated compared to a typical Central…

Computational Engineering, Finance, and Science · Computer Science 2015-01-30 Ru Zhu

We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…

Numerical Analysis · Mathematics 2023-08-24 Kai Bergermann , Martin Stoll

This paper presents a novel, high-performance, graphical processing unit-based algorithm for efficiently solving two-dimensional linear programs in batches. The domain of two-dimensional linear programs is particularly useful due to the…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-14 John Charlton , Steve Maddock , Paul Richmond

An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…

Other Condensed Matter · Physics 2016-08-31 Taisuke Ozaki

The paper presents the aspect of use of modern graphics accelerators supporting CUDA technology for high-performance computing in the field of linear algebra. Fully programmable graphic cards have been available for several years for both…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-06-27 Lukasz Swierczewski

An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are…

Numerical Analysis · Mathematics 2020-05-08 Ronald B. Morgan , Travis Whyte , Walter Wilcox , Zhao Yang