Developing numerical libraries in Java

The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of compute-intensive applications now under development, particularly in science and engineering. In this paper we address practical issues of the Java language and environment which have an effect on numerical library design and development. Benchmarks which illustrate the current levels of performance of key numerical kernels on a variety of Java platforms are presented. Finally, a strategy for the development of a fundamental numerical toolkit for Java is proposed and its current status is described.Comment: 11 pages. Revised version of paper presented to the 1998 ACM Conference on Java for High Performance Network Computing. To appear in Concurrency: Practice and Experienc

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

MLI: An API for Distributed Machine Learning

MLI is an Application Programming Interface designed to address the challenges of building Machine Learn- ing algorithms in a distributed setting based on data-centric computing. Its primary goal is to simplify the development of high-performance, scalable, distributed algorithms. Our initial results show that, relative to existing systems, this interface can be used to build distributed implementations of a wide variety of common Machine Learning algorithms with minimal complexity and highly competitive performance and scalability

A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Forward-Mode Automatic Differentiation in Julia

We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as Python and MATLAB, ForwardDiff takes advantage of just-in-time (JIT) compilation to transparently recompile AD-unaware user code, enabling efficient support for higher-order differentiation and differentiation using custom number types (including complex numbers). For gradient and Jacobian calculations, ForwardDiff provides a variant of vector-forward mode that avoids expensive heap allocation and makes better use of memory bandwidth than traditional vector mode. In our numerical experiments, we demonstrate that for nontrivially large dimensions, ForwardDiff's gradient computations can be faster than a reverse-mode implementation from the Python-based autograd package. We also illustrate how ForwardDiff is used effectively within JuMP, a modeling language for optimization. According to our usage statistics, 41 unique repositories on GitHub depend on ForwardDiff, with users from diverse fields such as astronomy, optimization, finite element analysis, and statistics. This document is an extended abstract that has been accepted for presentation at the AD2016 7th International Conference on Algorithmic Differentiation.Comment: 4 page