CUBE: An Information-optimized parallel Cosmological $N$-body Algorithm

Cosmological large scale structure $N$-body simulations are computation-light, memory-heavy problems in supercomputing. The considerable amount of memory is usually dominated by an inefficient way of storing more than sufficient phase space information of particles. We present a new parallel, information-optimized, particle-mesh-based $N$-body code CUBE, in which information-efficiency and memory-efficiency are increased by nearly an order of magnitude. This is accomplished by storing particle's relative phase space coordinates instead of global values, and in the format of fixed point as light as 1 byte. The remaining information is given by complementary density and velocity fields (negligible in memory space) and proper ordering of particles (no extra memory). Our numerical experiments show that this information-optimized $N$-body algorithm provides accurate results within the error of the particle-mesh algorithm. This significant lowering of the memory-to-computation ratio breaks the bottleneck of scaling up and speeding up large cosmological $N$-body simulations on multi-core and heterogeneous computing systems.