Time-domain formulation of an edge source integral equation

Abstract

In computer simulations of sound in enclosures, diffraction components can be added to geometrical acoustics ones for increased accuracy. A computational problem with diffraction is the large number of higher-order terms that is generated. A recent frequency-domain edge source integral equation (ESIE) efficiently handles the sum of all higher-order diffraction for rigid, external scattering objects, while computing first-order diffraction separately. Here, a time-domain formulation of the same ESIE is presented. An initial version handles higher-order diffraction for separate scattering objects, such as stage ceiling reflectors, and the extension to general geometries is outlined. With this approach, in a first step an incident transient sound field is computed at discretized edge points, including the outgoing directivity. In a second step, the effects of diffraction of arbitrarily high order is handled by solving the IE iteratively, yielding the complete edge source time signals. In a third step, the edge source signals are propagated to receiver points. Numerical issues will be discussed, including discretization strategies and how to handle shadow zone boundary singularities. © 2013 Acoustical Society of America.