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Abstract : |
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. |
