Elastic behavior of a two--dimensional lattice beam.
Elastic membrane equation in bounded and unbounded domains.
Elastic wave equation
The goal of this talk is to describe the Lamé operator which drives the propagation of linear elastic waves. The main motivation for me is the work I have done in collaboration with Michel Campillo’s group from LGIT (Grenoble) on passive imaging in seismology. From this work, several mathematical problems emerged: equipartition of energy between and waves, high frequency description of surface waves in a stratified medium and related inverse spectral problems.We discuss the following topics:What...
Elastic wave propagation in parallel: the Huygens' approach.
The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...
Elastoplastic reaction of a container to water freezing
The paper deals with a model for water freezing in a deformable elastoplastic container. The mathematical problem consists of a system of one parabolic equation for temperature, one integrodifferential equation with a hysteresis operator for local volume increment, and one differential inclusion for the water content. The problem is shown to admit a unique global uniformly bounded weak solution.
Elasto-plastic torsion problem as an infinity Laplace's equation.
Electrical Impedance Tomography: from topology to shape
Electrical impedance tomography in nonlinear media
Electromagnetic fields in linear and nonlinear chiral media: a time-domain analysis.
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electroosmotic pumping in rectangular microchannels: a numerical treatment by the finite element method.
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
Elementary proofs of some basic subtemperature theorems
We present simple elementary proofs of several theorems about temperatures and subtemperatures. Most of these are concerned with mean values over heat spheres, heat balls, and modified heat balls, with applications to proving Harnack theorems and the monotone approximation of subtemperatures by smooth subtemperatures.
Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
Éléments finis et problèmes elliptiques dégénérés
Elements of a qualitative theory of Hamiltonian PDEs.
Eliciting harmonics on strings
One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at . The 'correct touch' is that b for which the modes, that do not vanish at , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree ....
Eliptické parciální diferenciální rovnice s degenerovanými koeficienty
Elliptic and degenerate-elliptic operators in unbounded domains