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The training process of neural networks is known to be time-consuming, and having a deep architecture only aggravates the issue. This process consists mostly of matrix operations, among which matrix multiplication is the bottleneck. Several…

Machine Learning · Computer Science 2025-06-17 Sana Ebrahimi , Rishi Advani , Abolfazl Asudeh

We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…

Programming Languages · Computer Science 2021-11-17 Ningning Xie , Tamara Norman , Dominik Grewe , Dimitrios Vytiniotis

Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…

Data Structures and Algorithms · Computer Science 2020-09-17 Abdurrahman Yaşar , Muhammed Fatih Balin , Xiaojing An , Kaan Sancak , Ümit V. Çatalyürek

The growing demand for real-time DNN applications on edge devices necessitates faster inference of increasingly complex models. Although many devices include specialized accelerators (e.g., mobile GPUs), dynamic control-flow operators and…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-12-15 Chong Tang , Hao Dai , Jagmohan Chauhan

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-02-09 Matteo Ceccarello , Andrea Pietracaprina , Geppino Pucci , Eli Upfal

Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…

Performance · Computer Science 2025-09-03 Esmail Abdul Fattah , Hatem Ltaief , Havard Rue , David Keyes

We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these…

Optimization and Control · Mathematics 2026-03-09 Shaked Regev , Nai-Yuan Chiang , Eric Darve , Cosmin G. Petra , Michael A. Saunders , Kasia Świrydowicz , Slaven Peleš

We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…

Numerical Analysis · Mathematics 2018-06-27 Timo Heister , Thomas Wick

In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…

Numerical Analysis · Computer Science 2015-04-23 AmirHossein Aminfar , Eric Darve

To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…

Computational Engineering, Finance, and Science · Computer Science 2021-04-29 Zhenqi Wang , Sebastian Wende-von Berg , Martin Braun

In this work, we study the accuracy and efficiency of hierarchical matrix ($\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known…

Numerical Analysis · Mathematics 2017-10-25 Stéphanie Chaillat , Luca Desiderio , Patrick Ciarlet

Algorithms for extracting hydrologic features and properties from digital elevation models (DEMs) are challenged by large datasets, which often cannot fit within a computer's RAM. Depression filling is an important preconditioning step to…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-08-17 Richard Barnes

Maximizing parallelism level in applications can be achieved by minimizing overheads due to load imbalances and waiting time due to memory latencies. Compiler optimization is one of the most effective solutions to tackle this problem. The…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-29 Zahra Khatami , Hartmut Kaiser , J. Ramanujam

A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…

Mathematical Software · Computer Science 2007-05-23 Thomas Lippert , Nikolay Petkov , Paolo Palazzari , Klaus Schilling

We present scalable hybrid-parallel algorithms for training large-scale 3D convolutional neural networks. Deep learning-based emerging scientific workflows often require model training with large, high-dimensional samples, which can make…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-28 Yosuke Oyama , Naoya Maruyama , Nikoli Dryden , Erin McCarthy , Peter Harrington , Jan Balewski , Satoshi Matsuoka , Peter Nugent , Brian Van Essen

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher

Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…

Emerging Technologies · Computer Science 2018-08-31 Fabio L. Traversa , Massimiliano Di Ventra

Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…

Hierarchical least-squares programming (HLSP) is an important tool in optimization as it enables the stacking of any number of priority levels in order to reflect complex constraint relationships, for example in physical systems like…

Optimization and Control · Mathematics 2025-06-16 Kai Pfeiffer

Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…

Mathematical Software · Computer Science 2016-08-24 Mathias Jacquelin , Yili Zheng , Esmond Ng , Katherine Yelick