Exascale Sparse Eigensolver Developments for Quantum Physics Applications

Abstract

In the German Research Foundation (DFG) project ESSEX (Equipping Sparse Solvers for Exascale), we develop scalable sparse eigensolver libraries for large quantum physics problems. Partners in ESSEX are the Universities of Erlangen, Greifswald, Wuppertal, Tokyo and Tsukuba as well as DLR. The project pursues a coherent co-design of all software layers where a holistic performance engineering process guides code development across the classic boundaries of application, numerical method and basic kernel library. The basic building block library supports an elaborate MPI+X approach that is able to fully exploit hardware heterogeneity while exposing functional parallelism and data parallelism to all other software layers in a flexible way. The advanced building blocks were defined and employed by the developments at the algorithms layer. Here, ESSEX provides state-of-the-art library implementations of classic linear sparse eigenvalue solvers including block Jacobi-Davidson, Kernel Polynomial Method (KPM), and Chebyshev filter diagonalization (ChebFD) that are ready to use for production on modern heterogeneous compute nodes with best performance and numerical accuracy. Research in this direction included the development of appropriate parallel adaptive AMG software for the block Jacobi-Davidson method. Contour integral-based approaches were also covered in ESSEX and were extended in two directions: The FEAST method was further developed for improved scalability, and the Sakurai-Sugiura method (SSM) method was extended to nonlinear sparse eigenvalue problems. These developments were strongly supported by Japanese project partners from University of Tokyo, Computer Science, and University of Tsukuba, Applied Mathematics. The applications layer delivers scalable solutions for conservative (Hermitian) and dissipative (non-Hermitian) quantum systems with strong links to optics and biology and to novel materials such as graphene and topological insulators.