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An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions

Alfredo Bermúdez, Bibiana López-Rodríguez, Rodolfo Rodríguez, Pilar Salgado (2013)

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

The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space...

An effective global path planning algorithm with teaching-learning-based optimization

Emad Hazrati Nejad, Sevgi Yigit-Sert, Sahin Emrah Amrahov (2024)

Kybernetika

Due to the widespread use of mobile robots in various applications, the path planning problem has emerged as one of the important research topics. Path planning is defined as finding the shortest path starting from the initial point to the destination in such a way as to get rid of the obstacles it encounters. In this study, we propose a path planning algorithm based on a teaching-learning-based optimization (TLBO) algorithm with Bezier curves in a static environment with obstacles. The proposed...

An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows

Andrea Manzoni (2014)

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

We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier–Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [S. Deparis, SIAM J. Numer. Anal. 46 (2008) 2039–2067; A. Quarteroni and G. Rozza, Numer. Methods Partial Differ. Equ. 23 (2007) 923–948; K. Veroy and A.T. Patera, Int. J. Numer. Methods Fluids 47 (2005) 773–788]) to more general affine and nonaffine parametrizations (such as volume-based...

An electromagnetic damping machine: model, analysis and numerics

A. Buffa, Y. Maday, F. Rapetti (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene considerato il modello bidimensionale completo di sistema elettromagnetico in movimento: le equazioni dei campi elettromagnetici sono accoppiate con quelle della meccanica e il sistema così ottenuto risulta essere non lineare nell'accoppiamento. Vengono analizzate la buona posizione del problema e la regolarità della soluzione continua; si propone inoltre uno schema di discretizzazione di tipo esplicito. Si dimostra la buona posizione e la convergenza della formulazione discreta...

An existence result in nonlinear theory of electromagnetic fields

Dorin Iesan, Antonio Scalia (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper is concerned with the nonlinear theory of equilibrium for materials which do not conduct electricity. An existence and uniqueness result is established.

An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model

István Faragó, Ferenc Izsák, Tamás Szabó, Ákos Kriston (2013)

Open Mathematics

An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.

An optimum design problem in magnetostatics

Antoine Henrot, Grégory Villemin (2002)

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

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

An Optimum Design Problem in Magnetostatics

Antoine Henrot, Grégory Villemin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

Anisotropic inverse problems and Carleman estimates

David Dos Santos Ferreira (2007/2008)

Séminaire Équations aux dérivées partielles

This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...

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