In this thesis, we introduce the fundamental equations behind the estimation of the link budget in a communications channel, highlighting the key limitations of conventional systems. Furthermore, we investigate the use of reconfigurable intelligent surfaces as a modern method of overcoming obstruction losses, while making use of numerical methods and computational electromagnetics to understand its physical mechanism and probe its theory of operation. Additionally, a preprint on computational geometry is presented, applicable to the field of computational electromagnetics, enabling the simulation of systems such as reconfigurable intelligent surfaces using open-source tools. Lastly, we provide a tool for the physical optimization of radio-frequency networks, based on mathematical programming. Such a tool may be used for the optimization of reconfigurable intelligent surfaces, ultimately improving the communication channel between a transmitter and receiver.