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Complexity issues for the symmetric interval eigenvalue problem

Milan Hladík (2015)

Open Mathematics

We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error....

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...

Computing with the Square Root of NOT

De Vos, Alexis, De Beule, Jan, Storme, Leo (2009)

Serdica Journal of Computing

To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.

Concepts—An object-oriented software package for partial differential equations

Philipp Frauenfelder, Christian Lage (2002)

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

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such...

Concepts—An Object-Oriented Software Package for Partial Differential Equations

Philipp Frauenfelder, Christian Lage (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into ...

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...

Cover pages

(2008)

Programs and Algorithms of Numerical Mathematics

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