The Numerical Solution of the Exterior Impedance (Robin) Problem for the Helmholtz’s Equation via Modified Galerkin Method: Superllipsoid

This thesis focuses on finding the solution for the exterior Robin Problem for the Helmholtz Equation and therefore, determines how a convergent smooth surface depending on its outer shape, in this case the superellipsoid, responds to different outer waves. The primary purpose is to calculate the possibility of a certain object, acquiring sufficient conditions, to either submerge under respectively high water pressure or maintain in outer space; if applicable, this approach can be used for a new efficient design of a portion of a submarine or part of a space craft, the second of more interest to NASA, one of my sponsors. In this thesis, I analyze the numerical solution for the Helmholtz equation in 3 Dimensions, for the superellipsoid for the Robin Boundary Condition and answer the question of how a surface reacts to incoming waves approaching from various directions. Would the object tend to the extremes of either absorbing or reflecting everything with which it comes into contact, or would it obtain a neutral combination of the two