Scalability of high-performance PDE solvers. (September 2020) - Fischer, Paul; Min, Misun; Rathnayake, Thilina; Dutta, Som; Kolev, Tzanio; Dobrev, Veselin; Camier, Jean-Sylvain; Kronbichler, Martin; Warburton, Tim; Świrydowicz, Kasia; Brown, Jed
Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p -type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h -type finite elements.