English
Related papers

Related papers: A Two-level GPU-Accelerated Incomplete LU Precondi…

200 papers

A litany of theoretical and numerical results have established the sketch-and-precondition paradigm as a powerful approach to solving large linear regression problems in standard computing environments. Perhaps surprisingly, much less work…

Data Structures and Algorithms · Computer Science 2025-06-09 Tyler Chen , Pradeep Niroula , Archan Ray , Pragna Subrahmanya , Marco Pistoia , Niraj Kumar

This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in $H(\mathrm{div})$. The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have…

Numerical Analysis · Mathematics 2024-11-22 Will Pazner , Tzanio Kolev , Panayot Vassilevski

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…

Geophysics · Physics 2020-01-22 M. A. Sbai , A. Larabi

This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. The key technical feature of HYLU is the…

Hardware Architecture · Computer Science 2026-04-02 Xiaoming Chen

This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain…

Numerical Analysis · Computer Science 2015-06-02 Ruipeng Li , Yousef Saad

We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…

Optimization and Control · Mathematics 2026-05-15 Pengyu Zhang , Ruiwei Jiang

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

The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the…

Numerical Analysis · Mathematics 2024-09-18 Li Zhao , Chen-Song Zhang , Chun-Sheng Feng , Shi Shu

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…

Numerical Analysis · Mathematics 2022-08-04 Atsushi Suzuki

The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few…

Numerical Analysis · Computer Science 2011-09-20 Murat Manguoglu

In sparse LU factorization, nonzero elements after symbolic factorization tend to distribute in diagonal and right-bottom region of sparse matrices. However, regular 2D blocking on this non-uniform distribution structure may lead to…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-12-05 Zhen Hu , Dongliang Xiong , Kai Huang , Changjun Wu , Xiaowen Jiang

The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-14 Manasi Tiwari , Sathish Vadhiyar

In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS.…

Optimization and Control · Mathematics 2025-11-25 Alexis Montoison , François Pacaud , Sungho Shin , Mihai Anitescu

The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…

Numerical Analysis · Mathematics 2018-09-19 Navneet Pratap Singh , Kapil Ahuja

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-20 Yu-Hang Tang , Oguz Selvitopi , Doru Popovici , Aydın Buluç

The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…

Optimization and Control · Mathematics 2025-05-21 Shaohui Yang , Toshiyuki Ohtsuka , Brian Plancher , Colin N. Jones

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…

Performance · Computer Science 2025-01-07 Esmail Abdul Fattah , Hatem Ltaief , Havard Rue , David Keyes

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

Numerical Analysis · Mathematics 2026-05-29 Yonghan Sun , Hou-Duo Qi , Deren Han , Jiaxin Xie

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

Machine Learning · Computer Science 2025-11-03 Zherui Yang , Zhehao Li , Kangbo Lyu , Yixuan Li , Tao Du , Ligang Liu

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

Numerical Analysis · Mathematics 2018-05-08 Ali Karakus , Noel Chalmers , Kasia Swirydowicz , Timothy Warburton