Accelerating Cosmic Microwave Background map-making procedure through preconditioning

TL;DR

This paper introduces advanced iterative solvers with novel preconditioning techniques that significantly accelerate the process of creating sky maps from CMB data, making it more efficient for large datasets.

Contribution

The work presents new parallel two-level preconditioners for conjugate gradient methods, improving convergence speed and robustness in CMB map-making.

Findings

Up to 5 times faster convergence compared to standard solvers

Reduced solution time by up to 4 times without extra memory overhead

Enhanced stability and robustness across various data sets

Abstract

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.