On the use of co-ordinate stretching in the numeral computation of high frequency scattering†

The scattering of the sound of a jet engine by an airplane fuselage is modelled by solving the axially symmetric Helmholtz equation exterior to a long thin ellipsoid. The integral equation method based on the single layer potential formulation is used. A family of coordinate systems on the body is introduced and an algorithm is presented to determine the optimal co-ordinate system. Numerical results verify that the optimal choict enables the solution to be computed with a grid that is coarse relative to the wavelength.