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Title: A Numerical Soft Fault Model for Iterative Linear Solvers.


Abstract not provided.

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Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: Proposed for presentation at the International ACM Symposium on High-Performance Parallel and Distributed Computing held June 17-19, 2015 in Portland, Oregon.
Country of Publication:
United States

Citation Formats

Elliott, James John,, Mueller, Frank, and Hoemmen, Mark Frederick. A Numerical Soft Fault Model for Iterative Linear Solvers.. United States: N. p., 2015. Web.
Elliott, James John,, Mueller, Frank, & Hoemmen, Mark Frederick. A Numerical Soft Fault Model for Iterative Linear Solvers.. United States.
Elliott, James John,, Mueller, Frank, and Hoemmen, Mark Frederick. 2015. "A Numerical Soft Fault Model for Iterative Linear Solvers.". United States. doi:.
title = {A Numerical Soft Fault Model for Iterative Linear Solvers.},
author = {Elliott, James John, and Mueller, Frank and Hoemmen, Mark Frederick},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2015,
month = 3

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  • Abstract not provided.
  • The connection between the solution of linear systems of equations by both iterative methods and explicit time stepping techniques is investigated. Based on the similarities, a suite of Runge-Kutta time integration schemes with extended stability domains are developed using Chebyshev iteration polynomials. These Runge-Kutta schemes are applied to linear and non-linear systems arising from the numerical solution of PDE`s containing either physical or artificial transient terms. Specifically, the solutions of model linear convection and convection-diffusion equations are presented, as well as the solution of a representative non-linear Navier-Stokes fluid flow problem. Included are results of parallel computations.
  • In this paper we consider the numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. In this paper we shall examine the error to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. Our conclusion is that errormore » is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). we describe this method, also commenting on Richardson's method and its advantages for large problems. We then apply Richardson's method and the Chebyshev method with the Manteuffel algorithm to the solution of the nonlinear equations by Newton's method. 25 refs.« less
  • Abstract not provided.