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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'
Reconstructing Rational Functions with
We present the open-source library for the
reconstruction of multivariate rational functions over finite fields. We
discuss the involved algorithms and their implementation. As an application, we
use in the context of integration-by-parts reductions and
compare runtime and memory consumption to a fully algebraic approach with the
program .Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio
A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems
In this paper, we discuss numerical methods for solving large-scale
continuous-time algebraic Riccati equations. These methods have been the focus
of intensive research in recent years, and significant progress has been made
in both the theoretical understanding and efficient implementation of various
competing algorithms. There are several goals of this manuscript: first, to
gather in one place an overview of different approaches for solving large-scale
Riccati equations, and to point to the recent advances in each of them. Second,
to analyze and compare the main computational ingredients of these algorithms,
to detect their strong points and their potential bottlenecks. And finally, to
compare the effective implementations of all methods on a set of relevant
benchmark examples, giving an indication of their relative performance
Computational linear algebra over finite fields
We present here algorithms for efficient computation of linear algebra
problems over finite fields
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