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Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics
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In this article, an augmented Lagrangian method for the solution of variational problems is proposed. But this method is not suitable for continuous media and their mathematical modeling, such as viscoplasticity and elastoviscasticity.Abstract:
1. Some continuous media and their mathematical modeling 2. Variational formulations of the mechanical problems 3. Augmented Lagrangian methods for the solution of variational problems 4. Viscoplasticity and elastoviscoplasticity in small strains 5. Limit load analysis 6. Two-dimensional flow of incompressible viscoplastic fluids 7. Finite elasticity 8. Large displacement calculations of flexible rods References Index.read more
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An inexact alternating direction method for solving a class of structured variational inequalities
TL;DR: Compared with the quadratic proximal alternating direction methods, the proposed method solves a series of related systems of nonlinear equations instead of aseries of sub-VIs and the convergence is proved under suitable conditions.
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An efficient and modular grad–div stabilization
TL;DR: Two modular grad–div algorithms for calculating solutions to the Navier–Stokes equations (NSE) are presented, adding to an NSE code a minimally intrusive module that implements grad-div stabilization.
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An ADMM-based interior-point method for large-scale linear programming
TL;DR: In this paper, a new framework to implement interior point method (IPM) in order to solve some very large-scale linear programs (LPs) is proposed, which is based on the Newton's method.
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A multilayer shallow model for dry granular flows with the $\mu(I)$ rheology: Application to granular collapse on erodible beds
TL;DR: In this paper, a multilayer shallow model is proposed to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology.
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