Raytracing in Galerkin Boundary Integral form

Abstract

Ray tracing is an established method for computing the late-time part of room impulse responses. But it has the drawback that only very crude Monte Carlo models of boundary scattering and diffraction are possible to include without losing its attractive computational cost scaling. This happens because higher-resolution models of these processes output multiple child rays for every parent ray received, making the number of rays grow with reflection order. An emerging solution is so-called 'Surface-Based' Geometrical Acoustics. Here the distribution of rays arriving at a boundary is mapped onto a predefined set of spatial elements and angular interpolation functions, producing a vector of coefficients. Re-radiation of subsequent reflections is then a matrix multiplication, with the steady state solution being solvable via a Neumann series. Since rays only every propagate one reflection order before being collected, diffraction and scattering process that cause them to multiply can be included without issue. Here we present a new formulation based on a Galerkin Boundary Element Method (BEM). A unique feature is its ability to readily change interpolation functions, so their effect on accuracy and convergence can be assessed. In this preliminary work, it is verified against an Image Source Model for a rectangular room.