Conformal method for the rectilinear digital waveguide mesh

The digital waveguide mesh (DWM) has proven to an efficient and accurate method for simulating multi-dimensional wave propagation in various applications such as physical modeling of musical instruments and room acoustics. However, problems appear when fitting a DWM to an arbitrary boundary because of the geometric constraints of a given mesh element. A finer mesh grid is often used in an attempt to resolve this situation, which entails an associated computational cost increase. This paper presents a conformal method for the rectilinear DWM as an efficient alternative. The proposed conformal method aims at better approximating rigid boundaries that are normally not well suited for a rectilinear DWM structure. It is inspired by the conformal method developed for the Finite Domain Time Difference (FDTD) scheme where a cell associated with the boundary is split with respect to a particular criterion and the material constant of the cell is adjusted accordingly [1]. By means of the interleaved waveguide network (IWN) [2], the conformal method is successfully achieved in the DWM.