FPGA-Based Calculator Using a CNN-UM Approach for Dynamical Systems Investigation

This work describes a distributed computing system, called DCMARK, aimed at solving partial dierential equations at the basis of many investigation elds such as Solid State Physics, Nuclear Physics and Plasma Physics. This dis- tributed architecture is based on the Cellular Neural Network (CNN) paradigm which allows to divide the dierential equation system solving into many parallel integration operations to be executed by a custom multiprocessor system. We pushed the number of processors to the limit of one processor for each equa- tion. In order to test the present idea, we chose to implement DCMARK on a single FPGA, designing the single processor in order to minimize its hardware requirements and to obtain a large number of easily interconnected processors. This approach is particularly suited to study the properties of one-, two- and three-dimensional locally interconnected dynamical systems. In order to test the computing platform, we implemented a 200 cells, Korteweg de Vries (KdV) equa- tion solver and performed a comparison between simulations conducted on high performance PC and on our system. Since our distributed architecture takes a constant computing time to solve the equation system, independently of the number of dynamical elements (cells) of the CNN array, it allows to reduce the elaboration time more than other similar systems in literature. To ensure a high level of recongurability, we designed a compact System on Programmable Chip (SoPC) managed by a softcore processor which controls the fast data/control communication between our system and a PC Host. An intuitively Graphical User Interface (GUI) allows to change the calculation parameters and plot the results.