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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'
Robust Preconditioners for Incompressible MHD Models
In this paper, we develop two classes of robust preconditioners for the
structure-preserving discretization of the incompressible magnetohydrodynamics
(MHD) system. By studying the well-posedness of the discrete system, we design
block preconditioners for them and carry out rigorous analysis on their
performance. We prove that such preconditioners are robust with respect to most
physical and discretization parameters. In our proof, we improve the existing
estimates of the block triangular preconditioners for saddle point problems by
removing the scaling parameters, which are usually difficult to choose in
practice. This new technique is not only applicable to the MHD system, but also
to other problems. Moreover, we prove that Krylov iterative methods with our
preconditioners preserve the divergence-free condition exactly, which
complements the structure-preserving discretization. Another feature is that we
can directly generalize this technique to other discretizations of the MHD
system. We also present preliminary numerical results to support the
theoretical results and demonstrate the robustness of the proposed
preconditioners
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
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