Highorder scheme implementation using NewtonKrylov solution methods
Abstract
Implementation of highorder 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, loworder preconditioning using a matrixfree method to approximate the action of the Jacobian, and defect correction or loworder Jacobian and preconditioning. The residual in each case employs highorder discretization to preserve the highorder solution. Two preconditioners, point incomplete lowerupper factorization ILU(k) and block incomplete lowerupper factorization BILU(k) for k = 0,1,2 were applied. Also, oneway multigriding and capping the inner iterations was applied to determine the behavior of the solution performance. It was determined that, overall, the configuration using loworder 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:

 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:
 AC0794ID13223
 Resource Type:
 Journal Article
 Journal Name:
 Numerical Heat Transfer. Part B, Fundamentals
 Additional Journal Information:
 Journal Volume: 31; Journal Issue: 3; Other Information: PBD: AprMay 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. Highorder scheme implementation using NewtonKrylov solution methods. United States: N. p., 1997.
Web. doi:10.1080/10407799708915111.
Johnson, R W, McHugh, P R, & Knoll, D A. Highorder scheme implementation using NewtonKrylov solution methods. United States. doi:10.1080/10407799708915111.
Johnson, R W, McHugh, P R, and Knoll, D A. Tue .
"Highorder scheme implementation using NewtonKrylov solution methods". United States. doi:10.1080/10407799708915111.
@article{osti_509272,
title = {Highorder scheme implementation using NewtonKrylov solution methods},
author = {Johnson, R W and McHugh, P R and Knoll, D A},
abstractNote = {Implementation of highorder 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, loworder preconditioning using a matrixfree method to approximate the action of the Jacobian, and defect correction or loworder Jacobian and preconditioning. The residual in each case employs highorder discretization to preserve the highorder solution. Two preconditioners, point incomplete lowerupper factorization ILU(k) and block incomplete lowerupper factorization BILU(k) for k = 0,1,2 were applied. Also, oneway multigriding and capping the inner iterations was applied to determine the behavior of the solution performance. It was determined that, overall, the configuration using loworder 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}
}