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Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

Xavier AntoineMarion Darbas — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, ...

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Mark AschMarion DarbasJean-Baptiste Duval — 2011

ESAIM: Control, Optimisation and Calculus of Variations

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing...

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Mark AschMarion DarbasJean-Baptiste Duval — 2011

ESAIM: Control, Optimisation and Calculus of Variations

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for...

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