scholarly journals Multilevel augmented Lagrangian solvers for overconstrained contact formulations

2021 ◽  
Vol 71 ◽  
pp. 175-184
Author(s):  
Rolf Krause ◽  
Martin Weiser
Keyword(s):  
Augmented Lagrangian ◽  
Contact Problems ◽  
Standard Test ◽  
Test Problems ◽  
Nonpenetration Condition ◽  
Body Contact ◽  
Contact Formulation ◽  
Simple Implementation ◽  
The Cost ◽  
High Computational Efficiency

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

scholarly journals Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals

2021 ◽  
Author(s):  
Jingmin Xia ◽  
Patrick E. Farrell ◽  
Florian Wechsung
Keyword(s):  
Liquid Crystals ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Mass Matrix ◽  
Unit Length ◽  
Mesh Size ◽  
Schur Complement ◽  
Cholesteric Liquid Crystals ◽  
Multigrid Algorithm ◽  
The Cost

AbstractWe propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic and cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

An Adaptive EFG-FE Computational Model for Thermal Elasto-Plastic Frictional Contact Problems

2008 ◽  
Vol 33-37 ◽  
pp. 821-826
Author(s):  
Zheng Zhang ◽  
Geng Liu ◽  
Tian Xiang Liu
Keyword(s):  
Frictional Heating ◽  
Contact Problems ◽  
Coupling Model ◽  
Adaptive Refinement ◽  
Frictional Heat ◽  
Plastic Behavior ◽  
Initial Stiffness ◽  
Gradient Based ◽  
Local Adaptive Refinement ◽  
The Cost

An adaptive meshless element-free Galerkin-finite element (EFG-FE) coupling model for thermal elasto-plastic contact problems is developed to investigate the influences of the steady-state frictional heating on the contact performance of two contacting bodies. The thermal elasto-plastic contact problems using the initial stiffness method is presented. The local adaptive refinement strategy and the strain energy gradient-based error estimation for EFG-FE coupling method are combined. The adaptive meshless model takes into account the temperature variation, micro plastic flow, and the coupled thermo-elasto-plastic behavior of the materials, considering the strain-hardening property of the materials and temperature-dependent yield strength. The adaptive model is verified through the contact analysis of a cylinder with an elasto-plastic plane. The thermal effects on the contact pressure, stresses distributions with certain frictional heat inputs are studied. The results show that the accuracy of the solutions from the adaptive refinement model is satisfactory but the cost of the CPU time is much less than that for the uniform refinement calculation.

A Boundary Element Method for Multi-Body Contact Problems and its Application to the Analysis of a Huge Excavator

1995 ◽  
Author(s):  
Chong-De Liu ◽  
Jiyuan Yu ◽  
Xiaoming Wang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Contact Problems ◽  
Fortran Program ◽  
Boundary Integral ◽  
Element Formulation ◽  
Body Contact ◽  
Boundary Integral Formulation ◽  
Discretization Technique ◽  
Multi Body

Abstract The derivation of a boundary integral formulation and discretization technique in terms of boundary elements for the solution of multi-body contact problems has been carried out. A FORTRAN program has been developed based on this boundary element formulation and has been applied to the stress analysis of a huge caterpillar excavator woth 16 m3 bucket capacity.

Use of ANCF Surface Geometry in the Rigid Body Contact Problems: Application to Railroad Vehicle Dynamics

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Martin B. Hamper ◽  
Cheng Wei ◽  
Ahmed A. Shabana
Keyword(s):  
Rigid Body ◽  
Thin Plate ◽  
Surface Model ◽  
Spatial Derivative ◽  
Plate Element ◽  
Surface Geometry ◽  
Body Contact ◽  
First Order ◽  
Contact Formulation ◽  
Railroad Vehicle

In the analysis of multibody system (MBS) dynamics, contact between two arbitrary rigid bodies is a fundamental feature in a variety of models. Many procedures have been proposed to solve the rigid body contact problem, most of which belong to one of the two categories: offline and online contact search methods. This investigation will focus on the development of a contact surface model for the rigid body contact problem in the case where an online three-dimensional nonconformal contact evaluation procedure, such as the elastic contact formulation—algebraic equations (ECF-A), is used. It is shown that the contact surface must have continuity in the second-order spatial derivatives when used in conjunction with ECF-A. Many of the existing surface models rely on direct linear interpolation of profile curves, which leads to first-order spatial derivative discontinuities. This, in turn, leads to erroneous spikes in the prediction of contact forces. To this end, an absolute nodal coordinate formulation (ANCF) thin plate surface model is developed in order to ensure second-order spatial derivative continuity to satisfy the requirements of the contact formulation used. A simple example of a railroad vehicle negotiating a turnout, which includes a variable cross-section rail, is tested for the cases of the new ANCF thin plate element surface, an existing ANCF thin plate element surface with first-order spatial derivative continuity, and the direct linear profile interpolation method. A comparison of the numerical results reveals the benefits of using the new ANCF surface geometry developed in this investigation.

The Design of Virtual Experiment Framework Based on ELVIS

2014 ◽  
Vol 1037 ◽  
pp. 161-164
Author(s):  
Dong Dong Li
Keyword(s):  
Simulation Experiment ◽  
Teaching Method ◽  
Standard Test ◽  
Virtual Experiment ◽  
Traditional Teaching ◽  
Virtual Instrumentation ◽  
Virtual Experiments ◽  
Function Modules ◽  
Innovation Ability ◽  
The Cost

The virtual simulation experiment framework consists of hardware and software function modules, which are both designed in this thesis. The application of virtual experiment framework has changed the traditional teaching method to a large extent, reduced the cost of laboratory construction and management, which is of the first importance to realize the remote experiment teaching. Through virtual experiments, students' interest in knowledge is cultivated and innovation ability is enhanced. With the National Instruments Educational Laboratory Virtual Instrumentation Suite (NI ELVIS) and LabVIEW, we could take advantage of graphical programming and a complete suite of standard test instruments on computer and directly interface these instruments to circuits, which is the base of virtual experiment framework.

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