Hierarchical Tree-Structures as Adaptive Meshes

Introduction: Two basic types of simulations exist for modeling systems of many particles: grid-based (point particles indirectly interacting with one another through the potential calculated from equivalent particle densities on a mesh) and particle-based (point particles directly interacting with a one another through potentials at their positions calculated from the other particles in the system). Grid-based solvers traditionally model continuum problems, such as fluid and gas systems, and mixed particle-continuum systems. Particle-based solvers find more use modeling discrete systems such as stars within galaxies or other rarefied gases. Many different physical systems, including electromagnetic interactions, gravitational interactions, and fluid vortex interactions, all are governed by Poisson\u27s Equation..