Performance Engineering for Exascale-Enabled Sparse Linear Algebra Building Blocks

Abstract

The increasing demand for solving larger and more complex problems in computational science and engineering is a major driving factor to deploy computer systems with ever-advancing performance capabilities. To increase the available performance, modern HPC platforms come with multiple levels of parallelism, complex memory hierarchies, heterogeneous architectures, and extreme scales. To match the need for sustainable and efficient software under these premises, special value has to be attached to the inherent challenges like efficiency on all scales and performance portability across heterogeneous architectures. This work addresses the development of high-performance scientific software for sparse linear algebra, which is an important field of research and forms the foundation of many applications of computational science and engineering, with a special focus on sparse eigenvalue solvers on current and future supercomputers. Consequent employment of performance models as well as a holistic view on applications, algorithms, and hardware architectures enable the creation of basic computational building blocks, custom compute kernels, and optimized algorithmic formulations with provably high efficiency. To demonstrate the applicability of the developed software components, full-application performance of selected sparse eigenvalue solvers for real-world problems on some of the world‘s largest supercomputers with completely different hardware architectures – including homogeneous multi-core CPU clusters, GPU-accelerated clusters, and selfhosted many-core CPU clusters – is presented.