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On the Multiscale Solution of Constrained Minimization Problems [chapter]

Rolf Krause
2008 Lecture Notes in Computational Science and Engineering  
Groß for his help in implementing the UG/Cubit Interface and the anonymous referees for their remarks.  ...  Consequently, a multigrid method can either be used as a solver or preconditioner for the linearized problem, or it can serve as a nonlinear solver by itself.  ...  For a nonlinear multigrid method for smooth problems we refer to [10] . We remark that the references given here are far from exhaustive and refer the reader to the references cited therein.  ... 
doi:10.1007/978-3-540-75199-1_8 fatcat:ofpuyslhwranpiqdv3lhjl7tua

A scalable TFETI algorithm for two-dimensional multibody contact problems with friction

Z. Dostál, T. Kozubek, P. Horyl, T. Brzobohatý, A. Markopoulos
2010 Journal of Computational and Applied Mathematics  
algorithms for bound and equality constrained problems.  ...  elasticity with the Coulomb friction and proved to be scalable for the Tresca friction.  ...  algorithm for contact problems with friction is a challenging task which requires identifying the contact interface in a sense for free.  ... 
doi:10.1016/j.cam.2010.05.042 fatcat:zhyuu4ux25e63a57rxd44icfbq

Efficient simulation of multi-body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

Thomas Dickopf, Rolf Krause
2009 International Journal for Numerical Methods in Engineering  
We enforce the discrete contact constraints by means of a non-conforming domain decomposition method, which allows for optimal error estimates.  ...  The emerging nonlinear system is solved by a monotone multigrid method of optimal complexity. Several numerical examples in 3D illustrate the effectiveness of our approach.  ...  The authors would like to thank Sebastian Paik for the implementation of the modified simplex algorithm and help with the integration of the octree component, the group of Hanns Ruder at University of  ... 
doi:10.1002/nme.2481 fatcat:44csrkjin5fgjfq7b3nxxxsemi

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

Jörg Frohne, Timo Heister, Wolfgang Bangerth
2015 International Journal for Numerical Methods in Engineering  
In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned  ...  This includes highly accurate solutions of a benchmark problem and scaling our methods to 1,024 cores and more than a billion unknowns.  ...  In order to solve it, we apply a single step of a primal-dual active set method that replaces it by an equality constrained problem where boundary displacements are prescribed on parts of the contact surface  ... 
doi:10.1002/nme.4977 fatcat:oytgrmg3aze6lfs2bnkygr2v5e

Variationally consistent discretization schemes and numerical algorithms for contact problems

Barbara Wohlmuth
2011 Acta Numerica  
Thus the analysis can be based on the constrained minimization problem (2.7) for contact without friction.  ...  Characteristically, this type of application leads to a constrained minimization problem or more generally to a variational inequality (Harker and Pang 1990, Haslinger, Hlavác̆ek, Nec̆as and Lovı́s̆ek  ... 
doi:10.1017/s0962492911000079 fatcat:yyysmpkqkbgyppr4awyqywrhom

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
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  ...  The contributions of this article are: 1) a novel, parallel implementation of a dual mortar method and non-smooth SQP method, 2) realistic rock geometries with rough surfaces, and 3) numerical examples  ...  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

PDE Acceleration: A convergence rate analysis and applications to obstacle problems [article]

Jeff Calder, Anthony Yezzi
2019 arXiv   pre-print
We then apply PDE acceleration to solve minimal surface obstacle problems, including double obstacles with forcing, and stochastic homogenization problems with obstacles, obtaining state of the art computational  ...  to obstacle problems.  ...  We proved convergence with a linear rate for this class of accelerated PDE's, and applied the method to minimal surface obstacle problems, including a double obstacle problem with forcing, and a stochastic  ... 
arXiv:1810.01066v2 fatcat:q23isnrunzh5dgjvlzccjjws2q

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The resulting linear systems are solved alternatively by the Multigrid method and Krylov subspace methods. We treat two types of boundary conditions: Dirichlet and natural boundary condition.  ...  The hybrid scheme is constructed in such a way that we can prove that it is stable. We can also show that it is high order accurate in smooth domains and oscillatory free close to the shock.  ...  To show the flexibility, we also generalize our results to two-body contact problems with Coulomb friction on non-matching meshes and to obstacle problems with two membrans.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

DiffPD: Differentiable Projective Dynamics [article]

Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, Wojciech Matusik
2021 arXiv   pre-print
We present a novel, fast differentiable simulator for soft-body learning and control applications.  ...  We also apply DiffPD in a reality-to-simulation (real-to-sim) example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.  ...  Levin, Bo Zhu, and Eftychios Sifakis for their feedback and suggestions on this paper. The duck and cow mesh models in Figs  ... 
arXiv:2101.05917v3 fatcat:7zvujof7mjc35a23jhlay2szs4

Scalable Total BETI based algorithm for 3D coercive contact problems of linear elastostatics

J. Bouchala, Z. Dostál, M. Sadowská
2009 Computing  
A Total BETI (TBETI) based domain decomposition algorithm with the preconditioning by a natural coarse grid of the rigid body motions is adapted for the solution of contact problems of elasticity and proved  ...  constrained problems.  ...  Acknowledgements This research has been financially supported by the grants GA CR 201/07/0294, AS CR 1ET400300415, and the Ministry of Education of the Czech Republic No. MSM6198910027.  ... 
doi:10.1007/s00607-009-0044-9 fatcat:67cuheff3jbb3naajtg6bjgp3u

DiffPD: Differentiable Projective Dynamics

Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, Wojciech Matusik
2022 ACM Transactions on Graphics  
We present a novel, fast differentiable simulator for soft-body learning and control applications.  ...  We also apply DiffPD in a reality-to-simulation ( real-to-sim ) example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.  ...  Levin, Bo Zhu, and Eftychios Sifakis for their feedback and suggestions on this article.  ... 
doi:10.1145/3490168 fatcat:aneexw3frjbadpekiwqt56x254

Mathematics as a Technology–Challenges for the next Ten Years [chapter]

H Neunzert
2005 Lecture Notes in Pure and Applied Mathematics  
Existence of such two regimes can be very essential for some applications of impinging jets, if the generated liquid fi lm can have a contact with obstacles.  ...  This makes the direct application of the FEM for the calculation of the contact problem prohibitively costly. A method is developed that allows deriving a macrocontact condition on the interface.  ...  The latter is related to the penetration front and a Stefan type problem is formulated to account for it. A fi nite-volume method is used to approximate the given differential problem.  ... 
doi:10.1201/9781420026511.pt1 fatcat:c6ni6noa3nambgkuftojudjbem

Towards an efficient numerical simulation of complex 3D knee joint motion

Oliver Sander, Corinna Klapproth, Jonathan Youett, Ralf Kornhuber, Peter Deuflhard
2013 Computing and Visualization in Science  
The large algebraic systems of the bone-cartilage contact problems are solved efficiently by the truncated non-smooth Newton multigrid method.  ...  For the time discretization of the elastic and viscoelastic parts we use a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method.  ...  For solving the discrete problems we combine a nonlinear Dirichlet-Neumann method for the coupled problem with the Truncated Nonsmooth Newton Multigrid (TNNMG) method for the contact problems.  ... 
doi:10.1007/s00791-014-0227-6 fatcat:ew3ygwat4zf77bbmh7z6djuh44

Spurious currents in finite element based level set methods for two-phase flow

Sara Zahedi, Martin Kronbichler, Gunilla Kreiss
2011 International Journal for Numerical Methods in Fluids  
Also, the Navier-Stokes group and the Parallel Scientific Computing Colloquium are acknowledged for being a platform for discussion and ideas.  ...  I am grateful to Wolfgang Bangerth for acting like a second adviser from afar, developing my knowledge on finite element programming.  ...  ), step-37 (multigrid solver based on cell-based finite element operator application), step-40 (a massively parallel Poisson solver), step-48 (parallel cell-based finite element operator application).  ... 
doi:10.1002/fld.2643 fatcat:lurcjd5gyzhanfvjb2rx6iacwi

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  between contact and friction.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa
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