Iterative map-making with two-level preconditioning for polarized Cosmic
  Microwave Background data sets
  An estimation of the sky signal from streams of Time Ordered Data (TOD)
acquired by 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 more challenging in terms of computational cost and memory
in particular in the context of ground based experiments. In this context, we
study a novel class of the Preconditioned Conjugate Gradient (PCG) solvers
which invoke two-level preconditioners. We compare them against PCG solvers
commonly used in the map-making context considering their precision and
time-to-solution. We compare these new methods on realistic, simulated data
sets reflecting the characteristics of current and forthcoming \cmb
ground-based experiment. We develop an embarrassingly parallel implementation
of the approach where each processor performs a sequential map-making for a
subset of the TOD. We find that considering the map level residuals the new
class of solvers permits achieving tolerance of up to 3 orders of magnitude
better than the standard approach, where the residual level often saturates
before convergence is reached. This corresponds to an important improvement in
the precision of recovered power spectra in particular on the largest angular
scales. The new method also typically requires fewer iterations to reach a
required precision and thus shorter runtimes 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, e.g., as in Monte Carlo simulations, this
cost has to be incurred only once, and the method should be competitive not
only as far as its precision but also its performance is concerned.
