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.