Adaptive rectangular decomposition: A spectral, domain-decomposition approach for fast wave solution on complex scenes

Computational wave propagation is increasingly becoming a practical tool for acoustic prediction in indoor and outdoor spaces, with applications ranging from noise control to architectural acoustics. We discuss Adaptive Rectangular Decomposition (ARD), that decomposes a complex 3D domain into a set of disjoint rectangular partitions. Assuming spatially-invariant speed of sound,spectral basis functions are derived from the analytic solution and used to time-step the field with high spatio-temporal accuracy within each partition. This allows close-to-Nyquist numerical grids, with as low as 3 points per wavelength, resulting in large performance gains of ten to hundred times compared to the Finite-Difference Time-Domain method. The coarser simulation grid also allows much larger computational domains. ARD employs finite-difference interface operators to transfer waves between adjoining rectangular partitions. We show that efficient, spatially-compact interface operators can be designed to ensure low numerical errors. Numerical solutions obtained with ARD are compared to analytical solutions on simple geometries and good agreement is observed.