Displaying 241 – 260 of 664

Showing per page

Interpolation of non-smooth functions on anisotropic finite element meshes

Thomas Apel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

Inverse du Laplacien discret dans le problème de Poisson-Dirichlet à deux dimensions sur un rectangle

Jean Chanzy (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Ce travail a pour objet l’étude d’une méthode de « discrétisation » du Laplacien dans le problème de Poisson à deux dimensions sur un rectangle, avec des conditions aux limites de Dirichlet. Nous approchons l’opérateur Laplacien par une matrice de Toeplitz à blocs, eux-mêmes de Toeplitz, et nous établissons une formule donnant les blocs de l’inverse de cette matrice. Nous donnons ensuite un développement asymptotique de la trace de la matrice inverse, et du déterminant de la matrice de Toeplitz....

Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data

Peng Gao, Heping Dong, Fuming Ma (2018)

Applications of Mathematics

We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...

Inverted finite elements : a new method for solving elliptic problems in unbounded domains

Tahar Zamène Boulmezaoud (2005)

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

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of n . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.

Inverted finite elements: a new method for solving elliptic problems in unbounded domains

Tahar Zamène Boulmezaoud (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of n . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.

Invisible obstacles

A. G. Ramm (2007)

Annales Polonici Mathematici

It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.

Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗

Yogi Erlangga, Eli Turkel (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...

Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗

Yogi Erlangga, Eli Turkel (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...

L p -inequalities for the laplacian and unique continuation

W. O. Amrein, A. M. Berthier, V. Georgescu (1981)

Annales de l'institut Fourier

We prove an inequality of the type | x | r f L p ( R n ) c ( n , p , q , r ) | x | τ + μ Δ f L q ( R n ) . This is then used to derive the unique continuation property for the differential inequality | Δ f ( x ) | | v ( x ) | | f ( x ) | under suitable local integrability assumptions on the function v .

Laplace type operators: Dirichlet problem

Wojciech Kozł (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into 𝖲𝖮 ( n ) -irreducible subspaces.

Currently displaying 241 – 260 of 664