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SUMMARY We perform here some meshfree methods to inhomogeneous Laplace equations. We prove the efficiency of those methods compared with classical ones, for one or two dimensional case for numerics, and for one dimensional for theorical results.
It is known that the solution of an elastic scattering problem behaves asymptotically like a sum of a spherical P wave and a spherical S wave. This result, as its acoustic counterpart either, is generally proved by way of some integral representation formula, which contains rather complicated terms in the elastic case. We adopt here a diierent viewpoint,… (More)
A generalization of Isakov's theorem ((13]) to admissible shapes that include screens with a Robin boundary condition (in which the impedance is also an unknown) is presented. We also establish a characterization that enables us to distinguish the far-eld of plane screens from others. Numerical results using a quasi-Newton method are presented.
It is known that hard planar acoustic screens generate null far-eld amplitude on the directions deened by the plane that encloses them. We proved in an earlier paper that this property actually characterizes plane screens among scatterers of any shape, and we generalized it to other boundary conditions. Furthermore it was proved that a single incident wave… (More)