Advances techniques for the direct, numerical solution of Poisson's equation
An Abbreviated Numerical Scheme for Linear Symmetric Hyperbolic Equations, n ... 2.
An alternating-direction iteration method for Helmholtz problems
An alternating-direction iterative procedure is described for a class of Helmholz-like problems. An algorithm for the selection of the iteration parameters is derived; the parameters are complex with some having positive real part and some negative, reflecting the noncoercivity and nonsymmetry of the finite element or finite difference matrix. Examples are presented, with an applications to wave propagation.
An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
An analytical approach for quasi-linear equation in second order.
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An error estimate for finite volume methods for the Stokes equations.
An incomplete-factorization preconditioning using repeated red-black ordering.
Analysis of patch substructuring methods
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...
Approximation des espaces harmoniques
Asymptotic Expansion for the Discretization Error in Linear Elliptic Boundary Value Problems on General Regions.
Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations.
Axissymmetric Free Surface Seepage
Behavior of plane relaxation methods as multigrid smoothers.
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Composite Mesh Difference Methods for Elliptic Boundary Value Problems.
COMSOL modelling for a water infiltration problem in an unsaturated medium.
Contribution à la résolution numérique des équations de Laplace et de la chaleur