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Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…

Numerical Analysis · Mathematics 2019-09-10 Thomas A. Manteuffel , Steffen Munzenmaier , John Ruge , Ben S. Southworth

Krylov methods are a key way of solving large sparse linear systems of equations, but suffer from poor strong scalabilty on distributed memory machines. This is due to high synchronization costs from large numbers of collective…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-03-14 Shelby Lockhart , Amanda Bienz , William Gropp , Luke Olson

Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \in \mathbb{R}^{n \times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners…

Numerical Analysis · Mathematics 2014-04-09 Davod Khojasteh Salkuyeh , Mohsen Hasani , Fatemeh Panjeh Ali Beik

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Computer Vision and Pattern Recognition · Computer Science 2018-02-26 D. Khuê Lê-Huu , Nikos Paragios

We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with asymmetric linear systems. We use fixed-order GMRES polynomials to approximate $A_\textrm{ff}^{-1}$ and we use these polynomials to build grid…

Computational Physics · Physics 2023-06-12 S. Dargaville , R. P. Smedley-Stevenson , P. N. Smith , C. C. Pain

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…

Numerical Analysis · Mathematics 2017-12-27 Gustavo Chávez , George Turkiyyah , Stefano Zampini , David Keyes

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…

Numerical Analysis · Mathematics 2023-07-25 Sean Hon , Jiamei Dong , Stefano Serra-Capizzano

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-28 Evan Coleman , Masha Sosonkina

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Machine Learning · Computer Science 2025-07-10 Jihao Andreas Lin

We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maximizing the (work) energy of a membrane governed by the…

Optimization and Control · Mathematics 2026-02-26 Chiu-Yen Kao , Seyyed Abbas Mohammadi , Braxton Osting

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…

Optimization and Control · Mathematics 2007-05-23 Steven J. Benson , Todd S. Munson

This paper applies the Anderson Acceleration (AA) technique to accelerate the Fenchel dual gradient method (FDGM) to solve constrained optimization problems over time-varying networks. AA is originally designed for accelerating fixed-point…

Optimization and Control · Mathematics 2026-01-21 Haijuan Liu , Xuyang Wu

We present the Anderson Accelerated Primal-Dual Hybrid Gradient (AA-PDHG), a fixed-point-based framework designed to overcome the slow convergence of the standard PDHG method for the solution of linear programming (LP) problems. We…

Optimization and Control · Mathematics 2025-08-12 Yingxin Zhou , Stefano Cipolla , Phan Tu Vuong

In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…

Computational Engineering, Finance, and Science · Computer Science 2024-10-30 Sandra Liz Simon , Nitin Kaistha , Vishal Agarwal

This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…

Numerical Analysis · Mathematics 2020-07-08 Iryna Kulchytska-Ruchka , Sebastian Schöps

We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov…

Optimization and Control · Mathematics 2016-10-20 Andrew Knyazev , Alexander Malyshev

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…

Computational Engineering, Finance, and Science · Computer Science 2023-08-17 Kasia Świrydowicz , Nicholson Koukpaizan , Tobias Ribizel , Fritz Göbel , Shrirang Abhyankar , Hartwig Anzt , Slaven Peleš

This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…

Numerical Analysis · Mathematics 2026-02-05 Cecilia Pagliantini , Federico Vismara

In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-09-03 Lev Kazakovtsev