  In this work, we propose an adaptive geometric multigrid method for the
solution of large-scale finite cell flow problems. The finite cell method seeks
to circumvent the need for a boundary-conforming mesh through the embedding of
the physical domain in a regular background mesh. As a result of the
intersection between the physical domain and the background computational mesh,
the resultant systems of equations are typically numerically ill-conditioned,
rendering the appropriate treatment of cutcells a crucial aspect of the solver.
To this end, we propose a smoother operator with favorable parallel properties
and discuss its memory footprint and parallelization aspects. We propose three
cache policies that offer a balance between cached and on-the-fly computation
and discuss the optimization opportunities offered by the smoother operator. It
is shown that the smoother operator, on account of its additive nature, can be
replicated in parallel exactly with little communication overhead, which offers
a major advantage in parallel settings as the geometric multigrid solver is
consequently independent of the number of processes. The convergence and
scalability of the geometric multigrid method is studied using numerical
examples. It is shown that the iteration count of the solver remains bounded
independent of the problem size and depth of the grid hierarchy. The solver is
shown to obtain excellent weak and strong scaling using numerical benchmarks
with more than 665 million degrees of freedom. The presented geometric
multigrid solver is, therefore, an attractive option for the solution of
large-scale finite cell problems in massively parallel high-performance
computing environments.
