Dr. Georg Hager
Erlangen National High Performance Computing Center (NHR@FAU)
This project developed and implemented an optimized, massively parallel version of Chebyshev filter diagonalization (ChebFD), an algorithm for the computation of entire blocks of eigenvalues and associated eigenvectors of a given Hamiltonian. Starting from a previous implementation, which already achieves high node-level efficiency by using the GHOST library, a new two-level parallelism was introduced into the ChebFD scheme. The two-level parallelism allows for variable distribution of the individual search space vectors and the entire search space onto the computing nodes. In this approach, the increased communication volume of orthogonalization, after application of the polynomial filter, has to be balanced against the communication overhead of matrix-vector multiplication during application of the polynomial filter. A detailed performance model was constructed which allows to predict and validate the expected optimization potential via two-level parallelization. The new implementation was tested with typical example matrices from fermionic (Hubbard model) and excitonic systems and showed speedups between 2x and 5x compared to the baseline version without a second level of parallelism.
The implementation is freely available to the community at: https://www.bitbucket.org/alvbit/twolayerfd.
A. Alvermann, G. Hager, and H. Fehske: Orthogonal layers of parallelism in large-scale eigenvalue computations. Submitted and currently under review. Preprint: https://arXiv.org/abs/2209.01974