Elliptical Region Of Support of Two Dimensional Zero One Function in Hadoop Bigdata

Elliptical Region Of Support of Two Dimensional Zero One Function in Hadoop Bigdata

Abstract:

The purpose of this study is the derivation of a closed-form formula for Greenrsquo;s function in elliptic coordinates that could be used for achieving an analytic solution for the second-order diffraction problem by elliptical cylinders subjected to monochromatic incident waves. In fact, Greenrsquo;s function represents the solution of the so-called locked wave component of the second-order velocity potential. The mathematical analysis starts with a proper analytic formulation of the second-order diffraction potential that results in the inhomogeneous Helmholtz equation. The associated boundary-value problem is treated by applying Greenrsquo;s theorem to obtain a closed-form solution for Greenrsquo;s function. Greenrsquo;s function is initially expressed in polar coordinates while its final elliptic form is produced through the proper employment of addition theorems