Notes On Partial Differential Equations III: Two Dirchlet Type Problems For Poisson's Equation
Notes on partial differential equations III: Two Dirichlet type problems for Poisson's equation.
Nouvelles formulations intégrales pour les problèmes de diffraction d’ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....
Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all...
Noyaux élémentaires d'équations aux dérivées partielles du premier ordre
Numerical computation of soliton dynamics for NLS equations in a driving potential.
Numerical solution of a three-dimensional integral equation
Numerical study of acoustic multiperforated plates
It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.