Related papers: A Task Parallel Orthonormalization Multigrid Metho…
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…
Parallel-in-time methods have shown success for reducing the simulation time of many time-dependent problems. Here, we consider applying the multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current model problem.
We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
This paper presents an efficient parallel Cholesky factorization and triangular solve algorithm for the Karush-Kuhn-Tucker (KKT) systems arising in multistage optimization problems, with a focus on model predictive control and trajectory…
Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks. While existing gradient manipulation methods often yield more balanced solutions than simple scalarization-based approaches, they…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…
Parallel real-time embedded applications can be modelled as directed acyclic graphs (DAGs) whose nodes model subtasks and whose edges model precedence constraints among subtasks. Efficiently scheduling such parallel tasks can be challenging…
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
Stochastic gradient descent~(SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD…
Distributed deep learning (DDL) is a promising research area, which aims to increase the efficiency of training deep learning tasks with large size of datasets and models. As the computation capability of DDL nodes continues to increase,…
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
In this paper, we focus on efficient methods to solve discretized linear systems obtained from eddy current optimal control problems in an all-at-once approach. We construct a new low-rank matrix equation method based on a special splitting…