Several of the top ranked supercomputers are based on the
hybrid architecture consisting of a large number of CPUs
and GPUs. Very high performance has been obtained for
problems with special structures, such as FFT-based image
processing or N-body based particle calculations. However,
for the class of problems described by partial differential
equations discretized by finite difference (or other mesh
based methods such as finite element) methods, obtaining
even reasonably good performance on a CPU/GPU cluster
is challenging. In this paper, we propose and test a hybrid
algorithm that matches the architecture of the cluster. The
scalability of the approach is realized by a domain decomposition
method, and the high performance on GPU is realized
by using a smoothed aggregation based algebraic multigrid
method. Incomplete factorization, which performs beautifully
on CPU but poorly on GPU, is completely avoided in
the approach. We report some numerical results obtained by
using up to 32 CPU/GPU pairs for solving a PDE problem
with up to 32 millions unknowns.