Studies of the formation of galaxies and of large-scale structure rely heavily on N-body simulations, which act as efficient laboratories to test and guide theoretical investigations, and to inform observational programs. Such simulations try to approximate the continuous distribution function (DF) that fully characterizes the system at hand, with a discrete sample of particles. This work will provide solid foundations for evaluation of theoretical models, by constructing efficient algorithms to evolve a cosmologically relevant DF in the full six-dimensional phase space, a rather daunting task made tractable by the growth in available computational power. The 6D problem will be approached via 1D and 4D. The research will create efficient computational tools of use in theoretical astrophysics, plasma physics and computational fluid dynamics. It will provide benchmark simulations of cosmological structure formation, and lead to innovations in geometrical algorithms for the study of certain types of surfaces.
The project will engage students at the American University of Beirut and neighboring universities in fundamental research work. This involvement will help to make scientific computing a mainstay of research and education at the University. The broad collaborative dimension of the research will qualify the students' otherwise rather narrow exposure to current scientific practice.