A nested iterative scheme for indefinite linear systems in particulate flows

Abdelkader Baggag, Ahmed Sameh

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

High fidelity large-scale direct numerical simulation of particulate flows is of great value in a variety of industrial applications. It is computationally intensive as it combines time integration, solving nonlinear algebraic equations, and the associated linear systems. The finite element discretization of the coupled system of PDEs on an unstructured grid using an arbitrary Lagrangian-Eulerian moving mesh technique leads to very large nonlinear systems that are linearized by a version of Newton's method. The linear algebraic systems (Jacobians) are sparse, nonsymmetric and indefinite, for which standard linear system solvers based on Krylov subspace methods generally fail to converge without appropriate preconditioners. The failure of Krylov methods in production codes is currently being addressed by reducing the size of the time step. This, however, leads to a very long simulation time, and therefore is not always a viable approach. In this study, we design a hybrid inner-outer iterative scheme for solving these indefinite systems which proves to be both efficient, robust and ideally suited for parallel computing platforms even with appropriate large time steps. Comparisons with Krylov subspace methods show the superiority of our proposed class of nested iterative schemes which is also scalable with respect to mesh size, and insensitive to changes in properties of the fluid-particles system.

Original languageEnglish
Pages (from-to)1923-1957
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Volume193
Issue number21-22
DOIs
Publication statusPublished - 28 May 2004
Externally publishedYes

Fingerprint

linear systems
particulates
Linear systems
mesh
Direct numerical simulation
Newton-Raphson method
Parallel processing systems
Nonlinear equations
Newton methods
Industrial applications
pulse detonation engines
Nonlinear systems
nonlinear systems
direct numerical simulation
nonlinear equations
Fluids
platforms
fluids
simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

A nested iterative scheme for indefinite linear systems in particulate flows. / Baggag, Abdelkader; Sameh, Ahmed.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 21-22, 28.05.2004, p. 1923-1957.

Research output: Contribution to journalArticle

@article{3a63d038ff3f4f6fbc3d26686e013855,
title = "A nested iterative scheme for indefinite linear systems in particulate flows",
abstract = "High fidelity large-scale direct numerical simulation of particulate flows is of great value in a variety of industrial applications. It is computationally intensive as it combines time integration, solving nonlinear algebraic equations, and the associated linear systems. The finite element discretization of the coupled system of PDEs on an unstructured grid using an arbitrary Lagrangian-Eulerian moving mesh technique leads to very large nonlinear systems that are linearized by a version of Newton's method. The linear algebraic systems (Jacobians) are sparse, nonsymmetric and indefinite, for which standard linear system solvers based on Krylov subspace methods generally fail to converge without appropriate preconditioners. The failure of Krylov methods in production codes is currently being addressed by reducing the size of the time step. This, however, leads to a very long simulation time, and therefore is not always a viable approach. In this study, we design a hybrid inner-outer iterative scheme for solving these indefinite systems which proves to be both efficient, robust and ideally suited for parallel computing platforms even with appropriate large time steps. Comparisons with Krylov subspace methods show the superiority of our proposed class of nested iterative schemes which is also scalable with respect to mesh size, and insensitive to changes in properties of the fluid-particles system.",
author = "Abdelkader Baggag and Ahmed Sameh",
year = "2004",
month = "5",
day = "28",
doi = "10.1016/j.cma.2003.12.051",
language = "English",
volume = "193",
pages = "1923--1957",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0374-2830",
publisher = "Elsevier",
number = "21-22",

}

TY - JOUR

T1 - A nested iterative scheme for indefinite linear systems in particulate flows

AU - Baggag, Abdelkader

AU - Sameh, Ahmed

PY - 2004/5/28

Y1 - 2004/5/28

N2 - High fidelity large-scale direct numerical simulation of particulate flows is of great value in a variety of industrial applications. It is computationally intensive as it combines time integration, solving nonlinear algebraic equations, and the associated linear systems. The finite element discretization of the coupled system of PDEs on an unstructured grid using an arbitrary Lagrangian-Eulerian moving mesh technique leads to very large nonlinear systems that are linearized by a version of Newton's method. The linear algebraic systems (Jacobians) are sparse, nonsymmetric and indefinite, for which standard linear system solvers based on Krylov subspace methods generally fail to converge without appropriate preconditioners. The failure of Krylov methods in production codes is currently being addressed by reducing the size of the time step. This, however, leads to a very long simulation time, and therefore is not always a viable approach. In this study, we design a hybrid inner-outer iterative scheme for solving these indefinite systems which proves to be both efficient, robust and ideally suited for parallel computing platforms even with appropriate large time steps. Comparisons with Krylov subspace methods show the superiority of our proposed class of nested iterative schemes which is also scalable with respect to mesh size, and insensitive to changes in properties of the fluid-particles system.

AB - High fidelity large-scale direct numerical simulation of particulate flows is of great value in a variety of industrial applications. It is computationally intensive as it combines time integration, solving nonlinear algebraic equations, and the associated linear systems. The finite element discretization of the coupled system of PDEs on an unstructured grid using an arbitrary Lagrangian-Eulerian moving mesh technique leads to very large nonlinear systems that are linearized by a version of Newton's method. The linear algebraic systems (Jacobians) are sparse, nonsymmetric and indefinite, for which standard linear system solvers based on Krylov subspace methods generally fail to converge without appropriate preconditioners. The failure of Krylov methods in production codes is currently being addressed by reducing the size of the time step. This, however, leads to a very long simulation time, and therefore is not always a viable approach. In this study, we design a hybrid inner-outer iterative scheme for solving these indefinite systems which proves to be both efficient, robust and ideally suited for parallel computing platforms even with appropriate large time steps. Comparisons with Krylov subspace methods show the superiority of our proposed class of nested iterative schemes which is also scalable with respect to mesh size, and insensitive to changes in properties of the fluid-particles system.

UR - http://www.scopus.com/inward/record.url?scp=1842788000&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842788000&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2003.12.051

DO - 10.1016/j.cma.2003.12.051

M3 - Article

AN - SCOPUS:1842788000

VL - 193

SP - 1923

EP - 1957

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 21-22

ER -