An Error-Controlled Fast Multipole Method and the Road to Exascale

Fast summation methods like the FMM are the backbone of a multitude of simulations in MD, astrophysics or plasma physics. The linear complexity with respect to the number of particles enables the simulation of very large particle ensembles within a user-defined accuracy range.The massive amount of available FLOPs in today's HPC systems led to a shift in the development. What started as a hunt for the least amount of FLOPs, has now moved to implementations that can utilize all available hierarchical parallelism in the system.In this talk we will focus on three main topics: 1.) The efficient mathematical formulation of an error controlled FMM. 2.) The efficient implementation to utilize parallelism. 3.) The road towards exascal