English
Related papers

Related papers: Delayed approximate matrix assembly in multigrid w…

200 papers

We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…

Logic in Computer Science · Computer Science 2017-10-17 Ruediger Ehlers , Bernd Finkbeiner

Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…

Computational Engineering, Finance, and Science · Computer Science 2024-12-12 Dinesh Parthasarathy , Tommaso Bevilacqua , Martin Lanser , Axel Klawonn , Harald Köstler

In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires…

Numerical Analysis · Mathematics 2020-10-28 Daniel Jodlbauer , Ulrich Langer , Thomas Wick

The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…

Numerical Analysis · Mathematics 2014-02-18 James Brannick , Karsten Kahl , Sonja Sokolovic

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that…

Computational Engineering, Finance, and Science · Computer Science 2026-03-19 Dinesh Parthasarathy , Wayne Mitchell , Arjun Gambhir , Harald Köstler , Ulrich Rüde

Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…

Numerical Analysis · Mathematics 2025-06-30 Yi Zong , Peinan Yu , Haopeng Huang , Zhengding Hu , Xinliang Wang , Qin Wang , Chensong Zhang , Xiaowen Xu , Jian Sun , Yongxiao Zhou , Wei Xue

Traditionally, the geometric multigrid method is used with nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, the non-nested multigrid…

Numerical Analysis · Mathematics 2024-12-17 Marco Feder , Luca Heltai , Martin Kronbichler , Peter Munch

This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe…

Numerical Analysis · Mathematics 2020-05-20 S. Dargaville , A. G. Buchan , R. P. Smedley-Stevenson , P. N. Smith , C. C. Pain

In this paper, we present an efficient adaptive multigrid strategy for the geometry optimization of large-scale three dimensional molecular mechanics. The resulting method can achieve significantly reduced complexity by exploiting the…

Computational Physics · Physics 2022-08-30 Kejie Fu , Mingjie Liao , Yangshuai Wang , Jianjun Chen , Lei Zhang

Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…

Computer Vision and Pattern Recognition · Computer Science 2025-12-25 Zeqing Song , Zhongmiao Yan , Junyuan Deng , Songpengcheng Xia , Xiang Mu , Jingyi Xu , Qi Wu , Ling Pei

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

Numerical Analysis · Mathematics 2022-05-31 Victor A. Paludetto Magri , Robert D. Falgout , Ulrike M. Yang

Vertex-patch smoothers are essential for the robust convergence of geometric multigrid methods in high-order finite element applications, yet their adoption is traditionally hindered by the prohibitive cost of solving local patch problems.…

Numerical Analysis · Mathematics 2025-12-03 Michał Wichrowski

Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…

Multiagent Systems · Computer Science 2020-08-28 Allan Costa , Benjamin Jenett , Irina Kostitsyna , Amira Abdel-Rahman , Neil Gershenfeld , Kenneth Cheung

Aiming to generate easy-to-handle assembly sequences for robotic assembly, this study tackles assembly sequence generation by considering two tradeoff objectives: (1) insertion conditions and (2) degrees of constraints among assembled…

Robotics · Computer Science 2021-11-18 Takuya Kiyokawa , Jun Takamatsu , Tsukasa Ogasawara

Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…

Numerical Analysis · Mathematics 2021-05-05 Alec Michael Dunton , Alireza Doostan

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…

Mathematical Software · Computer Science 2018-05-28 Nils Kohl , Dominik Thönnes , Daniel Drzisga , Dominik Bartuschat , Ulrich Rüde

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

Optimization and Control · Mathematics 2024-03-01 Alfredo Vitorino , Francisco A. M. Gomes

The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…

Graphics · Computer Science 2025-01-23 Xuan Huang , Will Usher , Valerio Pascucci

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Numerical Analysis · Mathematics 2019-06-26 Andrea Franceschini , Victor A. Paludetto Magri , Gianluca Mazzucco , Nicolò Spiezia , Carlo Janna