Path-following and augmented Lagrangian methods for contact problems in linear elasticity

DOI10.1016/j.cam.2006.04.017zbMath1119.49028OpenAlexW2135607011MaRDI QIDQ879269

Georg Stadler

Publication date: 11 May 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.04.017

zbMATH Keywords

contact problemsaugmented Lagrangianssemismooth Newton methodspath-followingactive setsprimal-dual methods

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Newton-type methods (49M15) Numerical methods based on nonlinear programming (49M37) Contact in solid mechanics (74M15) Variational principles of physics (49S05)

Related Items (25)

Boundary augmented Lagrangian method for the Signorini problem. ⋮ A mixed interface finite element for cohesive zone models ⋮ Numerical approximation of viscous contact problems applied to glacial sliding ⋮ Boundary augmented Lagrangian method for contact problems in linear elasticity ⋮ A survey on dual decomposition methods ⋮ Projection and self-adaptive projection methods for the Signorini problem with the BEM ⋮ An interior point method for isogeometric contact ⋮ On the control of time discretized dynamic contact problems ⋮ Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality ⋮ Uzawa block relaxation method for the unilateral contact problem ⋮ Path-following for optimal control of stationary variational inequalities ⋮ A variational statement of quasistatic ``rigid-deformable contact problems at large strain involving generalized forces and friction ⋮ Combined symmetric BEM and semi-smooth Newton method for the contact problems in linear elasticity of Yukawa type ⋮ A duality-based path-following semismooth Newton method for elasto-plastic contact problems ⋮ Alternating direction method of multiplier for the unilateral contact problem with an automatic penalty parameter selection ⋮ Path following methods for steady laminar Bingham flow in cylindrical pipes ⋮ An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves ⋮ A self-adaptive projection method for contact problems with the BEM ⋮ Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem ⋮ Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics ⋮ Boundary element and augmented Lagrangian methods for contact problem with Coulomb friction ⋮ Adaptive inexact semismooth Newton methods for the contact problem between two membranes ⋮ Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: adaptivity and inexact resolution ⋮ An accelerated method of Uzawa algorithm in contact problems ⋮ An augmented Lagrangian method for the Signorini boundary value problem with BEM

Uses Software

• FEMLAB

Cites Work

• Matlab implementation of the finite element method in elasticity
• Lectures on numerical methods for non-linear variational problems
• A mixed formulation for frictional contact problems prone to Newton like solution methods
• The regularization method for an obstacle problem
• Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
• On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction
• A primal--dual active set strategy for nonlinear multibody contact problems
• Interior Point Methods in Function Space
• Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
• Semismooth Newton Methods for Operator Equations in Function Spaces
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• Interior Methods for Nonlinear Optimization
• Path-following Methods for a Class of Constrained Minimization Problems in Function Space
• Averaging technique for FE -- a posteriori error control in elasticity. I: Conforming FEM
• Efficient contact solvers based on domain decomposition techniques.
• Adaptive multigrid methods for Signorini's problem in linear elasticity.
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