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We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…

Numerical Analysis · Mathematics 2017-12-21 Chao Chen , Hadi Pouransari , Sivasankaran Rajamanickam , Erik G. Boman , Eric Darve

Optimal multiple sequence alignment by dynamic programming, like many highly dimensional scientific computing problems, has failed to benefit from the improvements in computing performance brought about by multi-processor systems, due to…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-30 Manal Helal , Hossam El-Gindy , Lenore Mullin , Bruno Gaeta

In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…

Optimization and Control · Mathematics 2015-01-29 James Turner , Michal Kocvara , Daniel Loghin

There are billions of lines of sequential code inside nowadays' software which do not benefit from the parallelism available in modern multicore architectures. Automatically parallelizing sequential code, to promote an efficient use of the…

Programming Languages · Computer Science 2016-04-13 Alcides Fonseca , Bruno Cabral , João Rafael , Ivo Correia

This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems…

Data Structures and Algorithms · Computer Science 2010-06-11 Guy E. Blelloch , Kanat Tangwongsan

Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…

Machine Learning · Computer Science 2024-12-11 Rui Li , Song Wang , Chen Wang

We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…

Numerical Analysis · Mathematics 2024-10-04 Youssef Diouane , Selime Gürol , Oussama Mouhtal , Dominique Orban

To train modern large DNN models, pipeline parallelism has recently emerged, which distributes the model across GPUs and enables different devices to process different microbatches in pipeline. Earlier pipeline designs allow multiple…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-23 Ziyue Luo , Xiaodong Yi , Guoping Long , Shiqing Fan , Chuan Wu , Jun Yang , Wei Lin

The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…

Numerical Analysis · Mathematics 2014-07-21 Adriano Festa

In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…

Optimization and Control · Mathematics 2013-02-11 Quoc Tran Dinh , Ion Necoara , Moritz Diehl

In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…

Machine Learning · Computer Science 2025-07-15 Yan-Ting Chen , Hao-Wei Chen , Tsu-Ching Hsiao , Chun-Yi Lee

We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $\epsilon$-approximate packing and covering solvers which run in…

Data Structures and Algorithms · Computer Science 2015-11-23 Di Wang , Michael Mahoney , Nishanth Mohan , Satish Rao

Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…

Numerical Analysis · Mathematics 2017-03-14 Kai Yang , Hadi Pouransari , Eric Darve

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…

Optimization and Control · Mathematics 2018-03-07 Giorgos Stathopoulos , Colin N. Jones

A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…

Numerical Analysis · Mathematics 2023-11-10 Luling Cao , Jian Li , Zhangxin Chen , Guangzhi Du

On modern parallel architectures, the cost of synchronization among processors can often dominate the cost of floating-point computation. Several modifications of the existing methods have been proposed in order to keep the communication…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-12-10 Qinmeng Zou , Frederic Magoules

Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…

Numerical Analysis · Mathematics 2025-05-28 Marc A. Tunnell , David F. Gleich

A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-05-19 Ruhollah Tavakoli

Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…

Numerical Analysis · Mathematics 2023-10-17 Katherine J. Pearce , Chao Chen , Yijun Dong , Per-Gunnar Martinsson

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) $V$-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has…

Numerical Analysis · Mathematics 2023-11-29 Stephen Thomas , Arielle Carr , Paul Mullowney , Kasia Świrydowicz , Marc Day