Generalized method of moments: A boundary integral framework for adaptive analysis of acoustic scattering

Boundary integral equations (BIEs) find applications in problems ranging from sonar to medical diagnostics. The two ingredients of the BIE solution technique are (1) representation of the domain and (2) design of approximation spaces to represent physical quantities on the domain. These, in concert, affect accuracy and convergence of the simulation. This paper presents a framework that permits the development of a scheme for refinement (of size and order) in both geometry and function representations. Further, this permits flexibility in the types of basis functions that can be used. Capabilities of the proposed framework are shown via a number of numerical examples. (C) 2012 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4740488]