2HOT: An Improved Parallel Hashed Oct-Tree N-Body Algorithm for Cosmological Simulation

We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k ($2^{18}$) processors. We present error analysis and scientific application results from a series of more than ten 69 billion ($4096^3$) particle cosmological simulations, accounting for $4 \times 10^{20}$ floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.Comment: 12 pages, 8 figures, 77 references; To appear in Proceedings of SC '1

Platform independent profiling of a QCD code

The supercomputing platforms available for high performance computing based research evolve at a great rate. However, this rapid development of novel technologies requires constant adaptations and optimizations of the existing codes for each new machine architecture. In such context, minimizing time of efficiently porting the code on a new platform is of crucial importance. A possible solution for this common challenge is to use simulations of the application that can assist in detecting performance bottlenecks. Due to prohibitive costs of classical cycle-accurate simulators, coarse-grain simulations are more suitable for large parallel and distributed systems. We present a procedure of implementing the profiling for openQCD code [1] through simulation, which will enable the global reduction of the cost of profiling and optimizing this code commonly used in the lattice QCD community. Our approach is based on well-known SimGrid simulator [2], which allows for fast and accurate performance predictions of HPC codes. Additionally, accurate estimations of the program behavior on some future machines, not yet accessible to us, are anticipated

The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure