Spectral Methods
Evolution to Complex Geometries and Applications to Fluid Dynamics
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41 Result(s)
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R. Glowinski
Mathematics
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Article
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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Book
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Book
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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...
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Article
Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations
This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibri...
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Article
New Optimization Approach to Multiphase Flow
A new optimization formulation for simulating multiphase flow in porous media is introduced. A locally mass-conservative, mixed finite-element method is employed for the spatial discretization. An unconditiona...
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Article
A boundary multiplier/fictitious domain method for the steady incompressible Navier-Stokes equations
We analyze the error of a fictitious-domain method with boundary Lagrange multiplier. It is applied to solve a non-homogeneous steady incompressible Navier-Stokes problem in a domain with a multiply-connected...
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Article
Neumann Control of Unstable Parabolic Systems: Numerical Approach
The present article is concerned with the Neumann control of systems modeled by scalar or vector parabolic equations of reaction-advection-diffusion type with a particular emphasis on systems which are unstabl...
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Article
An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
We discuss in this article the numerical solution of the Cahn-Hilliard equation modelling the spinodal decomposition of binary alloys. The numerical methodology combines a second-order finite difference time d...
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Article
Error analysis of a fictitious domain method applied to a Dirichlet problem
In this paper, we analyze the error of a fictitious domain method with a Lagrange multiplier. It is applied to solve a non homogeneous elliptic Dirichlet problem with conforming finite elements of degree one o...
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Chapter
Application of Exact Controllability to the Computation of Scattering Waves
The main goal of this article is to discuss an application of the Hilbert Uniqueness Method of J.L. Lions to the simulation of the scattering of planar waves by either perfectly conducting or coated materials....
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Article
On exact and approximate boundary controllabilities for the heat equation: A numerical approach
The present article is concerned with the numerical implementation of the Hilbert uniqueness method for solving exact and approximate boundary controllability problems for the heat equation. Using convex duali...
