N-Body simulations are at the core of many applications in astrophysics, molecular dynamics, and vortex flow methods. Fast algorithms for computing n-body interactions rely on a hierarchical domain discretization coupled with a series representation of subdomains. This project investigates various issues related to hierarchical methods: it addresses issues relating to accuracy, piecewise bases, and computational complexity. Parallel formulations of these accelerated multipole techniques along with their applications in solving dense linear systems are being investigated.