Fast volumetric integral-equation solver for acoustic wave propagation through inhomogeneous media.

Elements are described of a volumetric integral-equation-based algorithm applicable to accurate large-scale simulations of scattering and propagation of sound waves through inhomogeneous media. The considered algorithm makes possible simulations involving realistic geometries characterized by highly subwavelength details, large density contrasts, and described in terms of several million unknowns. The algorithm achieves its competitive performance, characterized by O(N log N) solution complexity and O(N) memory requirements, where N is the number of unknowns, through a fast and nonlossy fast Fourier transform based matrix compression technique, the adaptive integral method, previously developed for solving large-scale electromagnetic problems. Because of its ability of handling large problems with complex geometries, the developed solver may constitute an efficient and high fidelity numerical simulation tool for calculating acoustic field distributions in anatomically realistic models, e.g., in investigating acoustic energy transfer to the inner ear via nonairborne pathways in the human head. Examples of calculations of acoustic field distribution in a human head, which require solving linear systems of equations involving several million unknowns, are presented.

Fast volumetric integral-equation solver for high-contrast acoustics.

An approach for solving volumetric integral equations in acoustics, applicable to problems involving large density contrasts, is described. While the conventional Lippmann-Schwinger integral equations become under such circumstances ill conditioned, the proposed approach reformulates them and casts them into an equivalent system of well-conditioned surface and volume integral equations. The corresponding fast solver [utilizing stiffness matrix compression based on fast Fourier transforms and characterized by O(N log N) solution complexity and storage requirements, where N is the number of unknowns] was enhanced to incorporate the proposed formulation. Features of the solution method and of the solver are illustrated on representative examples of numerically large problems.