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On an Inequality of C. Sundberg: A Computational Investigation via Nonlinear Programming
The main goal of this article is to discuss a numerical method for finding the best constant in a Sobolev type inequality considered by C. Sundberg, and originating from Operator Theory. To simplify the invest...
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Article
Numerical methods for a class of nonlinear integro-differential equations
In a previous article (Glowinski, J. Math. Anal. Appl. 41, 67–96, 1973) the first author discussed several methods for the numerical solution of nonlinear equations of the integro-differential type with periodic ...
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Chapter
Methodes Iteratives Duales Pour la Minimisation de Functionnelles Convexes
I1 arrive qu'on puisse associer á un problème d'optimisation “difficile” ( parce que la fonction á minimiser est non différentiable, ou parce que les contraintes sont non-triviales ) un problème d'optimisation...
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Article
Non-smooth SOR for L 1-Fitting: Convergence Study and Discussion of Related Issues
In this article, the denoising of smooth (H 1-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the c...
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Article
Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monge-Ampère equation
The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various...
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Chapter and Conference Paper
Domain Decomposition and Model Reduction of Systems with Local Nonlinearities
The goal of this paper is to combine balanced truncation model reduction and domain decomposition to derive reduced order models with guaranteed error bounds for systems of discretized partial differential equ...
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Chapter and Conference Paper
Numerical Study of Particle Migration in Tube and Plane Poiseuille Flows
The lateral migration of a single spherical particle in tube Poiseuille flow is simulated by ALE scheme, along with the study of the movement of a circular particle in plane Poiseuille flow with consistent dim...
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Chapter and Conference Paper
Domain Decomposition Methods for Wave Propagation in Heterogeneous Media
The main goal of this paper is to address the numerical solution of a wave equation with discontinuous coefficients by a finite element method using domain decomposition and semimatching grids. A wave equation...
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Chapter and Conference Paper
Domain Embedding/Controllability Methods for the Conjugate Gradient Solution of Wave Propagation Problems
The main goal of this paper is to discuss the numerical simulation of propagation phenomena for time harmonic electromagnetic waves by methods combining controllability and fictitious domain techniques. These ...
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Article
Numerical Simulation of the Sedimentation of Rigid Bodies in an Incompressible Viscous Fluid by Lagrange Multiplier/Fictitious Domain Methods Combined with the Taylor–Hood Finite Element Approximation
In this work we discuss an application of a distributed Lagrange multiplier based fictitious domain method, to the numerical simulation of the motion of rigid bodies settling in an incompressible viscous fluid...
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Article
Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach
This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of probl...
