Numerical algorithms for high-performance computational science

Abstract

<jats:p>A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers.</jats:p> <jats:p>This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.</jats:p>

Libkrylov: A modular open‐source software library for extremely large on‐the‐fly matrix computations

“…Linear equations and eigenvalue problems with large dimensionality, on the order of >10 6 degrees of freedom, and no special structure or sparsity arise in many scientific and engineering applications, for example, quantum chemical and materials science simulations, partial differential equation solvers, signal reconstruction, and machine learning applications. [1][2][3] Density functional calculations of light-induced processes in organic and semiconductor nanostructures have pushed the limit of quantum chemical studies to systems with 1000 or more atoms. Molecular and material property calculations in these systems amount to solving eigenvalue problems of dimension one billion or larger.…”

Impact of HPC and Automated CFD Simulation Processes on Virtual Product Development—A Case Study

“…In [9], for example, an approach to an automated CFD-based optimization is shown. With the rapid increase in performance of processor and memory technologies and current research in the HPC domain [10], further increases in efficiency and cost reductions are highly probable. Combined with progressive development of computational methodologies [11,12], this opens new potential for product development [13].…”

ARENA: Asynchronous Reconfigurable Accelerator Ring to Enable Data-Centric Parallel Computing

“…With the slowing down of Moore's Law [51], future computer systems will need to resort to domain-specific accelerators for continuous performance scaling [27], [63] under the same power envelope. This is especially the case for HPC and data centers, as we are quickly entering an era of extreme heterogeneity [71], characterized by cluster nodes integrating a multitude of cooperating accelerators [33], [38], [43], [61].…”

“…(2) If data is not locally available, during the long-time remote data fetching, the compute units can be idle; (2) Even worse, these idle units or idle nodes cannot be reclaimed for other tasks despite the node may hold their desired data. As emerging workloads become more dynamic and data-driven, decentralized asynchronous task management is highly desired, while data locality becomes a crucial factor for the system design [18], [27], [63]. This is largely due to the observation that the energy cost of data-movement significantly overweights the energy cost of computing them [34], [40], [50], which is particularly the case when migrating arXiv:2011.04931v1 [cs.DC] 10 Nov 2020 data through the interconnect network (e.g., the power budget is ∼5.5 watts per full bi-directional NVLink port [1]).…”