This chapter covers the two algorithms used for this work, a Biot–Savart algorithm capable of computing the velocity of each vortex point depending on the position of every vortex point, and an energy spectra algorithm which computes the distribution of energy across different length scales; these algorithms are explained with detailed information flowcharts. The chapter explains how these algorithms were parallelized using SIMD parallelization, comparing it to a different acceleration method, Fast Multipole Method, and explaining the acceleration achieved while introducing minimal errors in the system. This chapter also describes the numerical methods used to evolve the Schrödinger fluid vortex tangles in time and how the model was damped to avoid numerical instabilities without deleting important energy dynamics information at small scales. The desingularization of the Biot–Savart law (the case where a vortex point self-induces velocity) and the timestep size calculation is also covered.