Newton-Krylov-Schwarz: An Implicit Solver for CFD.

Abstract

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect correction approach, subdomain preconditioner consistency, sub domain preconditioner quality, and the effect of a coarse grid.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1995
Accession Number
ADA304217

Entities

People

  • David E. Keyes
  • V. Venkatakrishnan
  • Xiao-chuan Cai

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Aerodynamics
  • Algorithms
  • Boundaries
  • Computational Fluid Dynamics
  • Computations
  • Computer Science
  • Decomposition
  • Differential Equations
  • Engineering
  • Equations
  • Flow
  • Fluid Dynamics
  • Physics
  • Precision
  • Standards
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Parallel and Distributed Computing.