We present a method for applying implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has implicit and fully coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of surface tension force, which...

Arbitrary Lagrangian Eulerian (ALE) methods have existed for several decades. However, three-dimensional multi-material arbitrary Lagrangian Eulerian (MMALE) methods for unstructured grids are relatively new. MMALE algorithms provide the framework to model sections of a simulation as either Lagrangian, ALE, or Eulerian. In addition, sections of a simulation can switch in time between mesh motio...

The numerical simulation of the interaction between a free surface flow and a moving obstacle is considered for the analysis of hydroplaning flows. A new augmented Lagrangian method, coupled to fictitious domains and penalty methods, is proposed for the simulation of multiphase flows. The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting...

In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

A globally and quadratically convergent primal–dual augmented Lagrangian algorithm for equality constrained optimization Paul Armand & Riadh Omheni To cite this article: Paul Armand & Riadh Omheni (2015): A globally and quadratically convergent primal–dual augmented Lagrangian algorithm for equality constrained optimization, Optimization Methods and Software, DOI: 10.1080/10556788.2015.1025401 ...

A generally nonconvex optimization problem with equality constraints is studied. The problem is introduced as an “inf sup” of a generalized augmented Lagrangian function. A dual problem is defined as the “sup inf’ of the same generalized augmented Lagrangian. Sufftcient conditions are derived for constructing the augmented Lagrangian function such that the extremal values of the primal and dual...

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augm...

A progressive hedging method incorporated with self-concordant barrier functions has been developed by Zhao [23] for solving multistage stochastic programs. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smooths the Lagrangian dual function by self-concordant barrier functions. This paper discusses in detail the implementation of this method and reports...

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-no...