  Multigrid algorithms are among the fastest iterative methods known today for
solving large linear and some non-linear systems of equations. Greatly
optimized for serial operation, they still have a great potential for
parallelism not fully realized. In this work, we present a novel multigrid
algorithm designed to work entirely inside many-core architectures like the
graphics processing units (GPUs), without memory transfers between the GPU and
the central processing unit (CPU), avoiding low bandwitdth communications. The
algorithm is denoted as the high occupancy multigrid (HOMG) because it makes
use of entire grid operations with interpolations and relaxations fused into
one task, providing useful work for every thread in the grid. For a given
accuracy, its number of operations scale linearly with the total number of
nodes in the grid. Perfect scalability is observed for a large number of
processors.
