English
Related papers

Related papers: Exploring Parallel-in-Time Approaches for Eddy Cur…

200 papers

In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…

Numerical Analysis · Mathematics 2023-04-28 Gobinda Garai , Bankim C. Mandal

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought…

Machine Learning · Computer Science 2024-01-17 Yi Heng Lim , Qi Zhu , Joshua Selfridge , Muhammad Firmansyah Kasim

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

Numerical Analysis · Mathematics 2013-10-01 Markus Blatt , Olaf Ippisch , Peter Bastian

Deep neural networks with large model sizes achieve state-of-the-art results for tasks in computer vision (CV) and natural language processing (NLP). However, these large-scale models are too compute- or memory-intensive for…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-29 Yang Hu , Connor Imes , Xuanang Zhao , Souvik Kundu , Peter A. Beerel , Stephen P. Crago , John Paul N. Walters

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear…

Numerical Analysis · Mathematics 2021-08-03 Tommaso Buvoli , Michael L. Minion

The problem under consideration is that of time-harmonic eddy current problems in linear ferromagnetic materials surrounded by a dielectric medium with a smooth common interface. Assuming axisymmetric geometries and orthoradial axisymmetric…

Numerical Analysis · Mathematics 2023-02-22 Dima Abou El Nasser El Yafi , Victor Péron

In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress…

Numerical Analysis · Mathematics 2018-02-06 Manuel Borregales , Kundan Kumar , Florin Adrian Radu , Carmen Rodrigo , Francisco José Gaspar

Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…

Optimization and Control · Mathematics 2018-11-02 William Pettersson , Melih Ozlen

This paper proposes a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments. A novel concept of Time-Warped Grid is introduced to predict the pose of obstacles in the environment and avoid…

Robotics · Computer Science 2019-03-19 Siavash Farzan , Guilherme N. DeSouza

In this article, we introduce a novel parallel-in-time solver for nonlinear ordinary differential equations (ODEs). We state the numerical solution of an ODE as a root-finding problem that we solve using Newton's method. The affine…

Numerical Analysis · Mathematics 2025-11-04 Casian Iacob , Hassan Razavi , Simo Särkkä

Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the…

Optimization and Control · Mathematics 2022-04-14 Yangyang Xu , Yibo Xu , Yonggui Yan , Colin Sutcher-Shepard , Leopold Grinberg , Jie Chen

We investigate the problem of minimizing the expectation of smooth nonconvex functions in a distributed setting with multiple parallel workers that are able to compute stochastic gradients. A significant challenge in this context is the…

Optimization and Control · Mathematics 2025-06-16 Artavazd Maranjyan , Omar Shaikh Omar , Peter Richtárik

Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…

Numerical Analysis · Mathematics 2013-12-25 Tejas Ruparel , Azim Eskandarian , James Lee

We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids. The grid layout we consider consists of a nested hierarchy of fixed size,…

Mathematical Software · Computer Science 2017-03-10 Donna Calhoun , Carsten Burstedde

The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…

Numerical Analysis · Mathematics 2020-01-03 Francois P. Hamon , Martin Schreiber , Michael L. Minion

Contemporary macro energy systems modelling is characterized by the need to represent strategic and operational decisions with high temporal and spatial resolution and represent discrete investment and retirement decisions. This drive…

Optimization and Control · Mathematics 2025-10-31 Michael Lau , Filippo Pecci , Jesse D. Jenkins

Speeding up computationally expensive problems, such as numerical simulations of large micromagnetic systems, requires efficient use of parallel computing infrastructures. While parallelism across space is commonly exploited in…

Computational Physics · Physics 2023-10-19 Robert Kraft , Sabri Koraltan , Markus Gattringer , Florian Bruckner , Dieter Suess , Claas Abert

This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…

Numerical Analysis · Mathematics 2023-06-16 Daniel Kressner , Stefano Massei , Junli Zhu

This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…

Data Structures and Algorithms · Computer Science 2015-03-17 Richard P. Brent

This paper presents a method of performing topology optimisation of transient heat conduction problems using the parallel-in-time method Parareal. To accommodate the adjoint analysis, the Parareal method was modified to store intermediate…

Computational Engineering, Finance, and Science · Computer Science 2024-12-02 Magnus Appel , Joe Alexandersen