Equipping Sparse Solvers for Exascale (ESSEX / ESSEX II)

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

Equipping Sparse Solvers for Exascale - A Survey of the DFG Project ESSEX

The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution. 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. Within ESSEX the numerical methods cover both widely applicable solvers such as classic Krylov, Jacobi-Davidson or recent FEAST methods as well as domain specific iterative schemes relevant for the ESSEX quantum physics application. This presentation introduces the project structure and presents selected results which demonstrate the potential impact of ESSEX for efficient sparse solvers on highly scalable heterogeneous supercomputers. In the second project phase from 2016 to 2018, the ESSEX consortium will include partners from the Universities of Tokyo and of Tsukuba. Extensions of existing work will regard numerically reliable computing methods, scalability improvements by leveraging functional parallelism in asynchronous preconditioners, hiding and reducing communication cost, improving load balancing by advanced partitioning schemes, as well as the treatment of non-Hermitian matrix problems

GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained

Increasing the performance of the Jacobi-Davidson method by blocking

Block variants of the Jacobi-Davidson method for computing a few eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm, but are generally shunned because the total number of floating-point operations increases. In this paper we present the implementation of a block Jacobi-Davidson solver. By detailed performance engineering and numerical experiments we demonstrate that the increase in operations is typically more than compensated by performance gains on modern architectures, giving a method that is both more efficient and robust than its single vector counterpart