### A method for selecting chief points in acoustic scattering

#### Abstract

In this work, the nonuniqueness problem of solving surface integral equation of acoustic scattering is considered. The solution of the acoustic scattering integral equation is not unique at some frequencies. A unique solution can be obtained by adding some constraints to the problem at some interior points of the scatterer. The primary difficulty is the lack of formalized method for the selection on the interior points to guarantee uniqueness. A simplified method for selecting interior points for CHIEF method is proposed. The new augmented surface integral equation is successful in reducing the needed number of points to solve at the characteristic frequencies of the scattering problem where a unique solution does not exist. The implementation of the method exploits the earlier computations used in selecting the interior points. Numerical results are presented at some characteristic frequencies for an axisymmetric body. A comparitive analysis is also presented to evaluate the potential of the proposed method.

#### Keywords

Acoustic fields; Boundary value problems; Error analysis; Integral equations; Matrix algebra; Natural frequencies; Problem solving; Vectors; Acoustic radiation; Computational costs; Helmholtz integral equations; Surface integral equations

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