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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...

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli, Alberto Ferrero, Susanna Terracini (2011)

Journal of the European Mathematical Society

Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.

Bilevel Approach of a Decomposed Topology Optimization Problem

A. Makrizi, B. Radi (2010)

Mathematical Modelling of Natural Phenomena

In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed...

Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

Habib Ammari, Shari Moskow, Michael S. Vogelius (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.

Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

Habib Ammari, Shari Moskow, Michael S. Vogelius (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.

C++ tools to construct our user-level language

Frédéric Hecht (2002)

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

The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.

C++ Tools to construct our user-level language

Frédéric Hecht (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++ to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.

Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

Hoai-Minh Nguyen (2015)

Journal of the European Mathematical Society

This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...

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...

Computation of the fundamental solution of electrodynamics for anisotropic materials

Valery Yakhno, Handan Yaslan, Tatiana Yakhno (2012)

Open Mathematics

A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier transform....

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2001)

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

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...

Conical diffraction by multilayer gratings: A recursive integral equation approach

Gunther Schmidt (2013)

Applications of Mathematics

The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in ℝ 2 coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with...

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