Equipping Sparse Solvers for Exascale (ESSEX / ESSEX II)

Abstract

The ESSEX project is funded by the German DFG priority programme 1648 "Software for Exascale Computing" (SPPEXA). In 2016 it has entered its second funding phase, ESSEX-II. ESSEX investigated programming concepts and numerical algorithms for scalable, efficient and robust iterative sparse matrix applications on exascale systems. Starting with successful blueprints and prototype solutions identified in ESSEX-I, the second phase project ESSEX-II developed a collection of broadly usable and scalable sparse eigenvalue solvers with high hardware efficiency for the computer architectures to come. Project activities were organized along the traditional software layers of low-level parallel building blocks (kernels), algorithm implementations, and applications. The classic abstraction boundaries separating these layers were broken in ESSEX by strongly integrating objectives: scalability, numerical reliability, fault tolerance, and holistic performance and power engineering. 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. In addition, facilities for fully asynchronous checkpointing, silent data corruption detection and correction, performance assessment, performance model validation, and energy measurements are provided transparently. The advanced building blocks were defined and employed by the developments at the algorithms layer. Here, ESSEX-II 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-II 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 additional 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. This talk gives a survey on latest results of the ESSEX-II project.