A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction

To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows one to include magnetostrictive effects into the simulations. Existence of weak solutions has recently been shown in Carbou et al. (2011) (Global weak solutions for the Landau-Lifschitz equation with magnetostriction. Math. Meth. Appl. Sci., 34, 1274-1288). In our contribution, we give an alternate proof which additionally provides an effective numerical integrator. The latter is based on linear finite elements (FEs) in space and a linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear systems have to be solved per timestep, and the integrator fully decouples both equations. Finally, we prove unconditional convergence—at least of a subsequence—towards, and hence existence of, a weak solution of the coupled system, as timestep size and spatial mesh size tend to zero. We conclude the work with numerical experiments, which study the discrete blow-up of the LLG equation as well as the influence of the magnetostrictive term on the discrete blow-u

A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction

To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows one to include magnetostrictive effects into the simulations. Existence of weak solutions has recently been shown in Carbou et al. (2011) (Global weak solutions for the Landau-Lifschitz equation with magnetostriction. Math. Meth. Appl. Sci., 34, 1274-1288). In our contribution, we give an alternate proof which additionally provides an effective numerical integrator. The latter is based on linear finite elements (FEs) in space and a linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear systems have to be solved per timestep, and the integrator fully decouples both equations. Finally, we prove unconditional convergence—at least of a subsequence—towards, and hence existence of, a weak solution of the coupled system, as timestep size and spatial mesh size tend to zero. We conclude the work with numerical experiments, which study the discrete blow-up of the LLG equation as well as the influence of the magnetostrictive term on the discrete blow-u

An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction

The Landau-Lifshitz-Gilbert Equation describes the dynamics of ferromag- netism, where strong nonlinearity and non-convexity are hard to tackle. Based on the work of S.Bartels and A.Prohl "Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation" ([4]), we present in this report a fully implicit finite element scheme with exchange and magnetostriction. We verify unconditional convergence and present numerical example

Splitting Methods with Modified Potentials and Application to the Damped Wave Equation

In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient for operator splitting schemes of order higher than two", which was published by ELSEVIER in 2004. After a brief introduction and some preliminaries on fundamental aknownledged, namely the flow of a differential equation which will allow to construct splitting schemes, we start the third part of this work with some definitions and fundamental theorems for general splitting schemes. At the end of this section, we will look more carefully on some special schemes, with modified potentials. In the fourth part, we study and compare some of the different methods seen in the third part of this report on an ordinary separable differential equation. In fifth part, we use these splitting schemes on the damped wave equation and look at the conservation of the Energy. Finally, you will find the main MATLAB code in the annexe

Approximation numérique des écoulements turbulents dans des cuves d'électrolyse de l'aluminium

Aluminium is a metal extracted from bauxite ore using electrolysis process in cells of big size. A huge electric current goes in the cell through an electrolytic bath and aluminium liquid. These currents generate strong magnetic forces that allow the bath and the aluminium to move. A good knowledge of these turbulent flows is very important to optimize the process. The purpose of this thesis is to study and simulate turbulent flows in the aluminium smelting process. These flows are solved numerically with a finite element method. In particular, the Navier-Stokes equations for bifluid flows with free moving interface are solved numerically. In the first part of this work, we develop some mixing-length models that take into account the effects of the wall. A theoretical mathematical study shows the validity of these models and we give some recommendation on the choice of the parameters of the computation. In the second part we study the resolution of the Navier-Stokes equations. The study focuses on algorithms that decouple the computation of the speed and pressure, commonly called projection method or Chorin-Temam algorithm. The final section provides answers on the relevance of wall modelling and projection methods in numerical simulation of turbulent flows in the aluminium smelting process. In particular, we obtain a numerical model that produces a realistic flow with a reasonable CPU time and we discuss the choice of certain parameters involved in the different models

On Some Weighted Stokes Problems. Application on Smagorinsky Models

In this paper we study existence and uniqueness of weak solutions for some non-linear weighted Stokes problems using convex analysis. The characteri- zation of these considered equations is that the viscosity depends on the strain rate of the velocity field with a weight being a positive power of the distance to the boundary of the domain. These non-linear relations can be seen as a first approach of mixing-length eddy viscosity from turbulent modeling. A well known model is von Karman’s on which the viscosity depends on the square of the distance to the boundary of the domain. Numerical experiments conclude the work and show prop- erties from the theory

Japan: Die alternde Gesellschaft braucht Technologie-und Communityentwicklung

Angesichts des stark ausgeprägten Fachkräftemangels, die an sich keine japanische Besonderheit darstellt, ist das Interesse an der Forschung über Robotik und Smart Systemen besonders gross. In Japan werden Roboter seit längerem eingesetzt und scheinen akzeptierter als in der Schweiz. Besonders interessant ist deswegen der japanischen Einsatz von Smart Technologien in Bezug der Frage der Alterung der Bevölkerung