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Title: High-order scheme implementation using Newton-Krylov solution methods

Abstract

Implementation of high-order discretization for the convective transport terms in the inexact Newton method for a benchmark fluid flow and heat transfer problem using various solution configurations at two Reynolds numbers has been investigated. These configurations include fully consistent discretization of the Jacobian, preconditioner and residual of the Newton method, low-order preconditioning using a matrix-free method to approximate the action of the Jacobian, and defect correction or low-order Jacobian and preconditioning. The residual in each case employs high-order discretization to preserve the high-order solution. Two preconditioners, point incomplete lower-upper factorization ILU(k) and block incomplete lower-upper factorization BILU(k) for k = 0,1,2 were applied. Also, one-way multigriding and capping the inner iterations was applied to determine the behavior of the solution performance. It was determined that, overall, the configuration using low-order preconditioning with ILU(1), BILU(1), or BILU(2), mesh sequencing, and inner linear solve iterations capped at the same value of the dimension n, used with the GMRES(n) iterative solver (i.e., no restarts), performed best for time, memory, and robustness considerations.

Authors:
; ;  [1]
  1. Lockheed Idaho Technologies Co., Idaho Falls, ID (United States). Idaho National Engineering Lab.
Publication Date:
Sponsoring Org.:
USDOE Idaho Operations Office, Idaho Falls, ID (United States)
OSTI Identifier:
509272
DOE Contract Number:  
AC07-94ID13223
Resource Type:
Journal Article
Journal Name:
Numerical Heat Transfer. Part B, Fundamentals
Additional Journal Information:
Journal Volume: 31; Journal Issue: 3; Other Information: PBD: Apr-May 1997
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; FLUID FLOW; HEAT TRANSFER; NEWTON METHOD; NUMERICAL ANALYSIS; NONLINEAR PROBLEMS

Citation Formats

Johnson, R W, McHugh, P R, and Knoll, D A. High-order scheme implementation using Newton-Krylov solution methods. United States: N. p., 1997. Web. doi:10.1080/10407799708915111.
Johnson, R W, McHugh, P R, & Knoll, D A. High-order scheme implementation using Newton-Krylov solution methods. United States. doi:10.1080/10407799708915111.
Johnson, R W, McHugh, P R, and Knoll, D A. Tue . "High-order scheme implementation using Newton-Krylov solution methods". United States. doi:10.1080/10407799708915111.
@article{osti_509272,
title = {High-order scheme implementation using Newton-Krylov solution methods},
author = {Johnson, R W and McHugh, P R and Knoll, D A},
abstractNote = {Implementation of high-order discretization for the convective transport terms in the inexact Newton method for a benchmark fluid flow and heat transfer problem using various solution configurations at two Reynolds numbers has been investigated. These configurations include fully consistent discretization of the Jacobian, preconditioner and residual of the Newton method, low-order preconditioning using a matrix-free method to approximate the action of the Jacobian, and defect correction or low-order Jacobian and preconditioning. The residual in each case employs high-order discretization to preserve the high-order solution. Two preconditioners, point incomplete lower-upper factorization ILU(k) and block incomplete lower-upper factorization BILU(k) for k = 0,1,2 were applied. Also, one-way multigriding and capping the inner iterations was applied to determine the behavior of the solution performance. It was determined that, overall, the configuration using low-order preconditioning with ILU(1), BILU(1), or BILU(2), mesh sequencing, and inner linear solve iterations capped at the same value of the dimension n, used with the GMRES(n) iterative solver (i.e., no restarts), performed best for time, memory, and robustness considerations.},
doi = {10.1080/10407799708915111},
journal = {Numerical Heat Transfer. Part B, Fundamentals},
number = 3,
volume = 31,
place = {United States},
year = {1997},
month = {4}
}