An analytical approach for the solution of the hydrodynamic diffraction by arrays of elliptical cylinders

This paper presents a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by arrays of elliptical cylinders subjected to incident waves. The solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions. The main contribution herein is the employment of the so-called addition theorem for Mathieu functions, which for the purposes of the present work is properly modified and eventually expressed in terms of the even and odd periodic and radial Mathieu functions.