6 research outputs found
Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations
The first-order system LL* (FOSLL*) approach for general second-order
elliptic partial differential equations was proposed and analyzed in [10], in
order to retain the full efficiency of the L2 norm first-order system
least-squares (FOSLS) ap- proach while exhibiting the generality of the
inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the
div-curl system with added slack vari- ables, and hence it is quite
complicated. In this paper, we apply the FOSLL* approach to the div system and
establish its well-posedness. For the corresponding finite ele- ment
approximation, we obtain a quasi-optimal a priori error bound under the same
regularity assumption as the standard Galerkin method, but without the
restriction to sufficiently small mesh size. Unlike the FOSLS approach, the
FOSLL* approach does not have a free a posteriori error estimator, we then
propose an explicit residual error estimator and establish its reliability and
efficiency bound
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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'
Recommended from our members
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