Uzawa Block Relaxation Domain Decomposition Method for the Two-Body Contact Problem With Tresca Friction

We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration. The auxiliary unknowns are computed explicitly using Kuhn-Tucker conditions and Fenchel duality theory. Numerical experiments show the scalability of the domain decomposition algorithm on matching or nonmatching meshes for two- or three-dimensional contact problems

XFEM based fictitious domain method for linear elasticity model with crack

Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid re-meshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for illustrating the applicability of the method.Comment: 27 pages, 15 figure

An optimization method for the reduction of fertilization errors with centrifugal applicators

This paper discusses an optimization method for the spreading performed by centrifugal spreaders in order to minimize adverse environmental effects owing to application errors. A cost functional relying on a conventional simplified spread pattern model is proposed. In order to take into account the mechanical limits of the device, constraints are introduced. An augmented Lagrangian algorithm is implemented to compute an approximate solution. Numerical experiments show that application errors can be significantly reduced for parallel tracks within a main field body

Numerical methods for the Stokes and Navier-Stokes equations driven by threshold slip boundary conditions

International audienceIn this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternating direction method of multiplier together with finite element approximations. The solution of the Navier Stokes system combines finite element approximations, time discretization by operator splitting and augmented Lagrangian method. Numerical experiment results for two and three dimensional flow confirm the interest of these approaches

An Augmented Lagrangian Method for TVg + L1-norm Minimization

International audienceIn this paper, the minimization of a weighted total variation regularization term with L1 norm as the data fidelity term is addressed using Uzawa block relaxation methods. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property allows us to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. Moreover, we highlight the fact that an appropriate weighted total variation term, chosen according to the properties of the initial image, may provide not only a significant improvement of the results but also a geometric filtering of the image components

Mesh r-adaptation for unilateral contact problems

We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method

Numerical methods for the Stokes and Navier-Stokes equations driven by threshold slip boundary conditions

In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary condi- tions of friction type in two and three dimensions. To solve the Stokes system, we rst reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternating direction method of multiplier together with nite element approximations. The solution of the Navier Stokes system combines nite element approximations, time discretization by operator splitting and augmented Lagrangian method. Numerical experiment results for two and three dimensional ow con rm the interest of these approaches.National Research Foundation of South Africa, project 85796,N00401.http://www.elsevier.com/locate/cma2017-03-31hb2016Mathematics and Applied Mathematic

Analysis of Temperature-to-Polarization Leakage in BICEP3 and Keck CMB Data from 2016 to 2018

The Bicep/Keck Array experiment is a series of small-aperture refracting telescopes observing degree-scale Cosmic Microwave Background polarization from the South Pole in search of a primordial B-mode signature. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We use high-fidelity, in-situ measurements of the beam response to estimate the temperature-to-polarization (T → P) leakage in our latest data including observations from 2016 through 2018. This includes three years of Bicep3 observing at 95 GHz, and multifrequency data from Keck Array. Here we present band-averaged far-field beam maps, differential beam mismatch, and residual beam power (after filtering out the leading difference modes via deprojection) for these receivers. We show preliminary results of "beam map simulations," which use these beam maps to observe a simulated temperature (no Q/U) sky to estimate T → P leakage in our real data

Uzawa block relaxation method for the unilateral contact problem

AbstractWe present a Uzawa block relaxation method for the numerical resolution of contact problems with or without friction, between elastic solids in small deformations. We introduce auxiliary unknowns to separate the linear elasticity subproblem from the unilateral contact and friction conditions. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional yields a two-step iterative method with a linear elasticity problem as a main subproblem while auxiliary unknowns are computed explicitly. Numerical experiments show that the method are robust and scalable with a significant saving of computational time