  Most, if not all the modern scientific simulation packages utilize matrix
algebra operations. Among the operation of the linear algebra, one of the most
important kernels is the multiplication of matrices, dense and sparse. Examples
of application of such a kernel are in electronic structure calculations,
machine learning, data mining, graph processing, and digital signal processing.
Several optimized libraries exist that can achieve high-performance on
distributed systems. Only a few of them target distributed GPU-accelerated
systems. In most of the cases, these libraries are provided and optimized by
system vendors for their specific computer systems. In this paper, we present
the DBCSR library (Distributed Block Compressed Sparse Row) for the distributed
dense matrix-matrix multiplications. Although the library is specifically
designed for block-sparse matrix-matrix multiplications, we optimized it for
the dense case on GPU-accelerated systems. We show that the DBCSR outperforms
the multiplication of matrices of different sizes and shapes provided by a
vendor optimized GPU version of the ScaLAPACK library up to 2.5x (1.4x on
average).
