  We present a method for parallel block-sparse matrix-matrix multiplication on
distributed memory clusters. By using a quadtree matrix representation, data
locality is exploited without prior information about the matrix sparsity
pattern. A distributed quadtree matrix representation is straightforward to
implement due to our recent development of the Chunks and Tasks programming
model [Parallel Comput. 40, 328 (2014)]. The quadtree representation combined
with the Chunks and Tasks model leads to favorable weak and strong scaling of
the communication cost with the number of processes, as shown both
theoretically and in numerical experiments.
  Matrices are represented by sparse quadtrees of chunk objects. The leaves in
the hierarchy are block-sparse submatrices. Sparsity is dynamically detected by
the matrix library and may occur at any level in the hierarchy and/or within
the submatrix leaves. In case graphics processing units (GPUs) are available,
both CPUs and GPUs are used for leaf-level multiplication work, thus making use
of the full computing capacity of each node.
  The performance is evaluated for matrices with different sparsity structures,
including examples from electronic structure calculations. Compared to methods
that do not exploit data locality, our locality-aware approach reduces
communication significantly, achieving essentially constant communication per
node in weak scaling tests.
