District heating leverages centralised, high efficiency combined heat and power (CHP) systems. It uses waste heat to lower energy consumption and reduce greenhouse emissions. The system also supports renewable energy sources like geothermal and biomass, providing a sustainable heating alternative.

This report examines a nonlinear network of pressure and flow challenges. It focuses on enhancing the Newton-Raphson method and refining direct solving techniques for a single time-step. As net- works grow in complexity, efficient and effective solutions become crucial. Various strategies to speed up the Newton-Raphson algorithm in Gradyent’s heat network solver are discussed, where derivative calculations are straightforward. Both direct and iterative methods to improve the algorithm’s steps are explored. The effectiveness of these enhancements is tested and evaluated across networks of different sizes.sc