Domain decomposition method for the digital waveguide mesh

The digital waveguide mesh (DWM) is a discrete-time numerical method for modeling the propagation of traveling waves in multidimensional mechanical and acoustic systems. Despite the fact that the DWM is not as computationally efficient as a 1-D digital waveguide, it is still widely used for sound synthesis of musical instruments and for acoustical modeling of rooms because of the simplicity of the implementation. However, large-scale realization of the digital waveguide mesh is not adequate for many simulations because of its relatively high and direction-dependent dispersion error. The influence of dispersion error can be reduced by using a denser mesh structure though with extra computational costs. This paper presents a method for efficiently interconnecting rectangular DWM sub-domains of different mesh density. The method requires only small overlapped buffer regions to be added for each sub-domain. This allows the selective use of higher and lower density grids in a single simulation based on spatially-dependent dispersion error criteria.