Full parallel process for multidimensional wave digital filtering via multidimensional retiming technique

As an alternative approach to the numerical integration of PDEs representing physical systems, the MD-WDF techniques has become of importance due to its attractive features such as massive parallelism and high accuracy inherent in nature. Speed-up efficiencies in terms of achieving fully parallel computing were studied for a 2D-WDF model of the linear transmission line using the chained MD retiming technique. To further explore parallel processing in MD-WDF models using the same pipelining technique, this paper presents the full parallelism for a 3D-WDF model of the linearised shallow water equations (SWEs), which is important in fluid dynamics. Experimental results show that the 3D-WDF model can achieve its full parallelism provided that at most seven parallel processors are each able to implement one multiplication and one addition on one time unit. These results can be extended to nonlinear SWEs, which encounters huge amount of data handling and specific nonlinear optimization problems arising from system modelling.