Efficient isogeometric boundary element method for analysis of acoustic scattering from rigid bodies

Boundary integral analysis of scattering from rigid bodies is well known. Analysis often proceeds along the following lines: representation of the geometry using a collection of triangles, representation of physics using low order ansatz functions defined on each triangle, and then solving the resulting discrete system. This prescription for the common solution stands out in terms of the low-order approximation of both geometry and representation of physics; specifically, both are C⁰. Taking inspiration from computer graphics literature, a framework wherein continuity of representation (both geometry and physics) can be as high as C² is developed. In this paper, the steps necessary to develop such a iso-geometric (i.e., using the same basis functions for representing both geometry and physics) boundary integral solver are elucidated. In doing so, an efficient method based on a wideband fast multipole method to evaluate the required inner products and matrix vector products is proposed and demonstrated. Numerous examples are presented to highlight the benefits of the proposed approach.