Numerical algorithms for high-performance computational science.

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. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems.

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax = b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4 × - 5 × performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.

THE VIRTUAL INSTRUMENT: SUPPORT FOR GRID-ENABLED MCELL SIMULATIONS.

Ensembles of widely distributed, heterogeneous resources, or Grids, have emerged as popular platforms for large-scale scientific applications. In this paper we present the Virtual Instrument project, which provides an integrated application execution environment that enables end-users to run and interact with running scientific simulations on Grids. This work is performed in the specific context of MCell, a computational biology application. While MCell provides the basis for running simulations, its capabilities are currently limited in terms of scale, ease-of-use, and interactivity. These limitations preclude usage scenarios that are critical for scientific advances. Our goal is to create a scientific "Virtual Instrument" from MCell by allowing its users to transparently access Grid resources while being able to steer running simulations. In this paper, we motivate the Virtual Instrument project and discuss a number of relevant issues and accomplishments in the area of Grid software development and application scheduling. We then describe our software design and report on the current implementation. We verify and evaluate our design via experiments with MCell on a real-world Grid testbed.