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Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics

Mark F. Adams
2004 Numerical Linear Algebra with Applications  
The potential of these methods is investigated with their application to contact problems in solid mechanics.  ...  This paper develops a general framework for applying algebraic multigrid techniques to constrained systems of linear algebraic equations that arise in applications with discretized PDEs.  ...  Linear Algebra Appl. 2000; 00:1-6 Prepared using nlaauth.cls  ... 
doi:10.1002/nla.374 fatcat:korhfe34ibdblkchoikb5h7t2e

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

T. A. Wiesner, M. Mayr, A. Popp, M. W. Gee, W. A. Wall
2021 International Journal for Numerical Methods in Engineering  
In this article, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach.  ...  equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems.  ...  Meanwhile, many successful applications to small and large deformation contact problems can be found in the literature. 1, 20, 21, 23 Algebraic formulation of linear systems For efficient iterative  ... 
doi:10.1002/nme.6680 fatcat:3u5z2xdcvzbnldtrrx35owxzna

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations [article]

Tobias A. Wiesner and Matthias Mayr and Alexander Popp and Michael W. Gee and Wolfgang A. Wall
2021 arXiv   pre-print
In this paper, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach.  ...  equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems.  ...  Algebraic formulation of linear systems For efficient iterative solution strategies based on multigrid methods for nonlinear contact problems, one is primarily interested in the structure of the linear  ... 
arXiv:1912.09056v3 fatcat:4ore6ahxfjh2xlokdcyngmbcb4

Constrainable Multigrid for Cloth

Inyong Jeon, Kwang-Jin Choi, Tae-Yong Kim, Bong-Ouk Choi, Hyeong-Seok Ko
2013 Computer graphics forum (Print)  
Experiments are performed which show that the proposed method can solve the linear system up to 4-9 times faster in comparison with the modified preconditioned conjugate gradient method (MPCG) without  ...  Resolving constrains has been difficult in MG because there has been no clear way to transfer the constraints existing in the finest level mesh to the coarser level meshes.  ...  Soft Constraint Formulation To remedy this problem, we use soft constraints for our multigrid framework. In this section, we formulate the soft constrained linear system at the finest level.  ... 
doi:10.1111/cgf.12209 fatcat:tdkibwquo5cc3fcoksno6jzile

Multilevel augmented Lagrangian solvers for overconstrained contact formulations

Rolf Krause, Martin Weiser, Didier Auroux, Jean-Baptiste Caillau, Régis Duvigneau, Abderrahmane Habbal, Christine Malot, Olivier Pantz, Luc Pronzato, Ludovic Rifford, Roland Ruelle, Chiara Soresi
2021 ESAIM Proceedings and Surveys  
Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces.  ...  For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers.  ...  The latter ones exploit the structural similarity of contact problems to linear elliptic equations of solid mechanics, for which they are optimal.  ... 
doi:10.1051/proc/202171175 fatcat:s65g5ahg4vefpho6lz7s47gmem

Page 3376 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Finite element discretization of the corresponding variational problem or variational inequality leads to nonlinear algebraic systems or to linearly constrained nonlinear programming problems.  ...  Oden reviews recent work on the use of exterior penalty methods as a basis for finite element approximation of contact problems in linear elasticity.  ... 

A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method [article]

Hardik Kothari, Rolf Krause
2021 arXiv   pre-print
We employ an unfitted Finite Element (FE) framework for the discretization of the domains and develop a tailored, globally convergent, and efficient multigrid method for solving contact problems on the  ...  We reformulate the arising variational inequality problem as a quadratic minimization problem with linear inequality constraints.  ...  " Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization [186407]" Additionally, we would also like to gratefully  ... 
arXiv:2106.16107v1 fatcat:3arlcozs3nh5xjj77jw5eeadp4

Reviews and Descriptions of Tables and Books

1989 Mathematics of Computation  
The first four volumes were concerned with the general exposition of the method while the fifth volume specifically concentrated on problems in Solid Mechanics.  ...  Readers of Direct Methods for Sparse Matrices are assumed to be familiar with elementary linear algebra and to have some computing background.  ... 
doi:10.1090/s0025-5718-89-99843-8 fatcat:kditgrcr7jgtrilpcxqycsbehq

Efficient Algorithms for Problems with Friction

S. Hüeber, A. Matei, B. I. Wohlmuth
2007 SIAM Journal on Scientific Computing  
In this paper, a nonconforming discretization method for the frictional contact between two bodies subjected to antiplane shear deformation is considered.  ...  To solve the discrete nonlinear problem an inexact primal-dual active set strategy is introduced.  ...  for both linear and nonlinear solid mechanics.  ... 
doi:10.1137/050634141 fatcat:y7q36p47gvdidcoaoigq7wpqre

Page 4516 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
for linearized problems with live loads (pp. 343-351); T.  ...  The solution of the system of algebraic equations obtained to accuracy € requires order O(h~? In h—! Ine~") arithmetical operations.”  ... 

Newsletter on computational and applied mathematics

1996 Journal of Computational and Applied Mathematics  
In the concluding chapter, further applications of the Banach algebra approach for these problems are highlighted.  ...  The most prominent application of numerical methods for integral equations is dealt with in the final two chapters.  ... 
doi:10.1016/s0377-0427(96)90002-3 fatcat:c7wnexqhmnflbesoqdtipe7hiy

Contact between rough rock surfaces using a dual mortar method [article]

Cyrill von Planta and Daniel Vogler and Patrick Zulian and Martin O. Saar and Rolf Krause
2019 arXiv   pre-print
The mechanical behavior of fractures in solids, such as rocks, has strong implications for reservoir engineering applications.  ...  Here we present a novel discrete implementation of a dual mortar method and a non-smooth SQP solver, suitable for parallel computing, and apply it to a two body contact problem consisting of realistic  ...  Acknowledgements We gratefully acknowledge funding by the Swiss Competence Center for Energy Research -Supply of Electricity (SCCER-SoE), by the Werner Siemens-Stiftung (Werner Siemens Foundation) and  ... 
arXiv:1811.02914v2 fatcat:7osmwj6odfghlgbsta3xbkwsvy

A Reverse Augmented Constraint preconditioner for Lagrange multiplier methods in contact mechanics [article]

Andrea Franceschinia, Matteo Frigo, Carlo Janna, Massimiliano Ferronato
2021 arXiv   pre-print
Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems.  ...  Frictional contact is one of the most challenging problems in computational mechanics.  ...  Acknowledgements Portions of this work were performed within the 2020 INdAM-GNCS project "Optimization and advanced linear algebra for PDE-governed problems".  ... 
arXiv:2111.05599v1 fatcat:f6boeu5mqbbdneykzjca5ec5yu

Newsletter on computational and applied mathematics

1997 Journal of Computational and Applied Mathematics  
mechanics who are interested in the development, implementation and application of advanced methods for reliable mathematical simulation of structural and mechanical systems.  ...  techniques, applied to direct and inverse problems in: • Solid Mechanics • Heat and Mass Transfer • Environmental Engineering • Fluid Dynamics.  ... 
doi:10.1016/s0377-0427(97)90033-9 fatcat:wjovtr3ktzez3pvnsvdtpzz6ei

Implicit Contact Handling for Deformable Objects

Miguel A. Otaduy, Rasmus Tamstorf, Denis Steinemann, Markus Gross
2009 Computer graphics forum (Print)  
We show the application of our algorithm in challenging scenarios such as multi-layered cloth moving at high velocities, or colliding deformable solids simulated with large time steps.  ...  dynamics problem: a time stepping algorithm that robustly ensures non-penetration and progressively refines the formulation of constrained dynamics, and a new solver for large mixed linear complementarity  ...  We would also like to thank the members of the CG lab at ETH and the GMRV group at URJC.  ... 
doi:10.1111/j.1467-8659.2009.01396.x fatcat:yksloandnvflvdveccpzu6hfj4
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