Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets: A worked example for ground-based experiments

Context. An estimation of the sky signal from streams of time ordered data (TOD) acquired by the cosmic microwave background (CMB) experiments is one of the most important steps in the context of CMB data analysis referred to as the map-making problem. The continuously growing CMB data sets render the CMB map-making problem progressively more challenging in terms of computational cost and memory in particular in the context of ground-based experiments with their operational limitations as well as the presence of contaminants. Aims. We study a recently proposed, novel class of the Preconditioned Conjugate Gradient (PCG) solvers which invoke two-level preconditioners in the context of the ground-based CMB experiments. We compare them against the PCG solvers commonly used in the map-making context considering their precision and time-to-solution. Methods. We compare these new methods on realistic, simulated data sets reflecting the characteristics of current and forthcoming CMB ground-based experiments. We develop a divide-and-conquer implementation of the approach where each processor performs a sequential map-making for a subset of the TOD. Results. We find that considering the map level residuals, the new class of solvers permits us to achieve a tolerance that is better than the standard approach by up to three orders of magnitude, where the residual level often saturates before convergence is reached. This often corresponds to an important improvement in the precision of the recovered power spectra in particular on the largest angular scales. The new method also typically requires fewer iterations to reach a required precision and therefore shorter run times are required for a single map-making solution. However, the construction of an appropriate two-level preconditioner can be as costly as a single standard map-making run. Nevertheless, if the same problem needs to be solved multiple times, for example, as in Monte Carlo simulations, this cost is incurred only once, and the method should be competitive, not only as far as its precision is concerned but also its performance.