Application of Fast Multipole Methods to the NASA Fast Scattering Code

solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor. K = Number of receiver boxes for SLFMM discretization S K = Number of source boxes for SLFMM discretization n ˆ = Unit surface normal vector directed into the fluid c N = Number of collocation points on scattering surface(s) s N = Number of equivalent sources on source surface(s) inc p ' = Incident acoustic pressure scat p ' = Scattered acoustic pressure µ ν P = Associated Legendre function of degree ν and order µ q = Spherical harmonic expansion truncation number