Fast Iterative Integral Equation Solver for Acoustic Scattering by Inhomogeneous Objects Using the Butterfly Approximation

The acoustic scattering by highly inhomogeneous objects is analyzed by a method-of-moment solver for the volume integral equation. To enable the treatment of acoustically large scatterers of various topologies, the iterative numerical solution of the resulting system is accelerated via a kernel independent algebraic compression scheme: blocks of the hierarchically partitioned moment stiffness matrix are expressed in butterfly form that, for volume problems, scales favorably compared to the popular low-rank approximation. A detailed description of the algorithm, as implemented in this work, is provided. Validations of the numerical formulation, parameter tuning, and performance study of the fast method for acoustically large objects are presented, in various settings and for a range of examples, representative of biomedical and oceanographic applications.