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Abstract

The solution of (generalized) eigenvalue problems for symmetric or Hermitian
matrices is a common subtask of many numerical calculations in electronic
structure theory or materials science. Solving the eigenvalue problem can
easily amount to a sizeable fraction of the whole numerical calculation. For
researchers in the field of computational materials science, an efficient and
scalable solution of the eigenvalue problem is thus of major importance. The
ELPA-library is a well-established dense direct eigenvalue solver library,
which has proven to be very efficient and scalable up to very large core
counts. In this paper, we describe the latest optimizations of the ELPA-library
for new HPC architectures of the Intel Skylake processor family with an AVX-512
SIMD instruction set, or for HPC systems accelerated with recent GPUs. We also
describe a complete redesign of the API in a modern modular way, which, apart
from a much simpler and more flexible usability, leads to a new path to access
system-specific performance optimizations. In order to ensure optimal
performance for a particular scientific setting or a specific HPC system, the
new API allows the user to influence in straightforward way the internal
details of the algorithms and of performance-critical parameters used in the
ELPA-library. On top of that, we introduced an autotuning functionality, which
allows for finding the best settings in a self-contained automated way. In
situations where many eigenvalue problems with similar settings have to be
solved consecutively, the autotuning process of the ELPA-library can be done
"on-the-fly". Practical applications from materials science which rely on
so-called self-consistency iterations can profit from the autotuning. On some
examples of scientific interest, simulated with the FHI-aims application, the
advantages of the latest optimizations of the ELPA-library are demonstrated.