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Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2001)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the decay...

Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the...

Convergence and quasi-optimal complexity of a simple adaptive finite element method

Roland Becker, Shipeng Mao (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an adaptive stopping criterion for iterative solution which compares an estimator for the iteration error...

Effective computation of restoring force vector in finite element method

Martin Balazovjech, Ladislav Halada (2007)

Kybernetika

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...

Error Control and Andaptivity for a Phase Relaxation Model

Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam (2008)

Serdica Journal of Computing

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...

High order semi-lagrangian particle methods for transport equations: numerical analysis and implementation issues

G.-H. Cottet, J.-M. Etancelin, F. Perignon, C. Picard (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the definition, analysis and implementation of semi-Lagrangian methods as they result from particle methods combined with remeshing. We give a complete consistency analysis of these methods, based on the regularity and momentum properties of the remeshing kernels, and a stability analysis of a large class of second and fourth order methods. This analysis is supplemented by numerical illustrations. We also describe a general approach to implement these methods in the context...

Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth, Ferenc Izsák (2012)

Open Mathematics

We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging...

Currently displaying 41 – 60 of 97