Asymptotic analysis for the solution to the Helmholtz problem in the exterior of a finite thin straight wire

Xavier Claeys (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

In this document we are interested in the solution of the Helmholtz equation with Dirichlet boundary condition in the exterior of a thin elongated body. We suppose that the geometry is well described in ellipsoidal coordinates. We propose an asymptotic analysis of this problem, using matched expansions. This leads to the construction of an approximate field with more explicit expression. The approximate field is composed of the first terms of the asymptotic expansion of the exact solution. Our study also leads to a validation of an acoustic version of the Pocklington's equation.

Mots clés: Helmholtz; asymptotic; Pocklington; wire; thin; matched expansions; elongated

Domaines: Analyse numérique [math.NA]

Xavier Claeys. Asymptotic analysis for the solution to the Helmholtz problem in the exterior of a finite thin straight wire. [Research Report] RR-6277, INRIA. 2007. ⟨inria-00163230v4⟩