The Abacus cosmological N-body code

We present Abacus, a fast and accurate cosmological N-body code based on a new method for calculating the gravitational potential from a static multipole mesh. The method analytically separates the near- and far-field forces, reducing the former to direct 1/r2 summation and the latter to a discrete convolution over multipoles. The method achieves 70 million particle updates per second per node of the Summit supercomputer, while maintaining a median fractional force error of 10−5. We express the simulation time step as an event-driven “pipeline”, incorporating asynchronous events such as completion of co-processor work, Input/Output, and network communication. Abacus has been used to produce the largest suite of N-body simulations to date, the AbacusSummit suite of 60 trillion particles (Maksimova et al., 2021), incorporating on-the-fly halo finding. Abacus enables the production of mock catalogs of the volume and resolution required by the coming generation of cosmological surveys.

Unified Vector Multiplication Approach for Calculating Convolution and Correlation

This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.