Fast multipole accelerated boundary element methods for room acoustics.

Direct and indirect boundary element methods, accelerated via the fast multipole method, are applied to numerical simulation of room acoustics for rooms of volume ∼150 m and frequencies up to 5 kHz on a workstation. As the parameter kD (wavenumber times room diameter) is large, stabilization of the previously developed fast algorithms is required for accuracy. A stabilization scheme is one of the key contributions of this paper.

Modes of self-organization of diluted bubbly liquids in acoustic fields: One-dimensional theory.

The paper is dedicated to mathematical modeling of self-organization of bubbly liquids in acoustic fields. A continuum model describing the two-way interaction of diluted polydisperse bubbly liquids and acoustic fields in weakly-nonlinear approximation is studied analytically and numerically in the one-dimensional case. It is shown that the regimes of self-organization of monodisperse bubbly liquids can be controlled by only a few dimensionless parameters.

Semi-analytical computation of acoustic scattering by spheroids and disks.

Analytical solutions to acoustic scattering problems involving spheroids and disks have long been known and have many applications. However, these solutions require special functions that are not easily computable. Therefore, their asymptotic forms are typically used instead since they are more readily available.

Hierarchical () computation of small-angle scattering profiles and their associated derivatives.

The need for fast approximate algorithms for Debye summation arises in computations performed in crystallography, small/wide-angle X-ray scattering and small-angle neutron scattering. When integrated into structure refinement protocols these algorithms can provide significant speed up over direct all-atom-to-all-atom computation. However, these protocols often employ an iterative gradient-based optimization procedure, which then requires derivatives of the profile with respect to atomic coordinates.

A hierarchical algorithm for fast Debye summation with applications to small angle scattering.

Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three-dimensional space, arises in computations performed in crystallography, small/wide angle X-ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ε in linear time.