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Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Yao-Chuang Han, Yu-Feng Nie, Zhan-Bin Yuan (2019)

Applications of Mathematics

This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm...

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)

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

This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in ℝ n (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc:= ℝ n ∖ Ω ¯ . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD)...

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM*

Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in ℝ n (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := ℝ n ∖ Ω ¯ . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2004)

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

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace’s equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace's equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Numerical study of a new global minimizer for the Mumford-Shah functional in R3

Benoît Merlet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In [Progress Math.233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in 𝐑 3 . The singular set of such a new minimizer belongs to a three parameters family of sets ( 0 < δ 1 , δ 2 , δ 3 < π ) . We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of 𝐒 2 with three reentrant corners. The necessary conditions are...

On the efficient use of the Galerkin-method to solve Fredholm integral equations

Wolfgang Hackbusch, Stefan A. Sauter (1993)

Applications of Mathematics

In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...

On the Schwarz algorithms for the elliptic exterior boundary value problems

Faker Ben Belgacem, Miche Fournié, Nabil Gmati, Faten Jelassi (2005)

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

Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...

Currently displaying 41 – 60 of 73