H-surface index formula
Hybrid level set phase field method for topology optimization of contact problems
The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...
Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆
In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Hyperfonctions et problèmes aux limites elliptiques
Hypersurfaces of constant curvature in hyperbolic space II
This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.
Hypersurfaces of Prescribed Mean Curvature over Obstacles.
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of critical curves. II. Discretization and numerical realization
We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.
Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals
In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate...
Implementing parallel elliptic solver on a Beowulf cluster.
Implicit a posteriori error estimation using patch recovery techniques
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...
Implicit second order partial differential equations
Improved Difference Schemes for the Dirichlet Problem of Poisson's Equation in the Neighbourhood of Corners.
Improved estimates for the Ginzburg-Landau equation : the elliptic case
We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
Incremental unknowns for solving partial differential equations.