### Abstract

We employ a damped Newton multigrid algorithm to solve a nonlinear system arising from a finite-difference discretization of an elliptic flame sheet problem. By selecting the generalized minimum residual method as the linear smoother for the multigrid algorithm, we conduct a series of numerical experiments to investigate the behavior and efficiency of the multigrid solver in solving the linearized systems, by choosing several preconditioners for the Krylov subspace method. It is shown that the overall efficiency of the damped Newton multigrid algorithm is highly related to the quality of the preconditioner chosen and the number of smoothing steps done on each level. ILU preconditioners based on the Jacobian pattern are found to be robust and provide efficient smoothing but at an expensive cost of storage. It is also demonstrated that the technique of mesh sequencing and multilevel correction scheme provides significant CPU saving for fine grid calculations by limiting the growth of the Krylov iterations.

Original language | English |
---|---|

Pages (from-to) | 269-279 |

Number of pages | 11 |

Journal | Mathematical and Computer Modelling |

Volume | 38 |

Issue number | 3-4 |

Publication status | Published - Sep 5 2003 |

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### Keywords

- ILU preconditioning
- Laminar diffusion flame
- Newton multigrid algorithm
- Nonlinear methods
- Vorticity-velocity formulation

### ASJC Scopus subject areas

- Information Systems and Management
- Control and Systems Engineering
- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

*Mathematical and Computer Modelling*,

*38*(3-4), 269-279.

**Preconditioned multigrid simulation of an axisymmetric laminar diffusion flame.** / Karaa, S.; Zhang, Jun; Douglas, C. C.

Research output: Contribution to journal › Article

*Mathematical and Computer Modelling*, vol. 38, no. 3-4, pp. 269-279.

}

TY - JOUR

T1 - Preconditioned multigrid simulation of an axisymmetric laminar diffusion flame

AU - Karaa, S.

AU - Zhang, Jun

AU - Douglas, C. C.

PY - 2003/9/5

Y1 - 2003/9/5

N2 - We employ a damped Newton multigrid algorithm to solve a nonlinear system arising from a finite-difference discretization of an elliptic flame sheet problem. By selecting the generalized minimum residual method as the linear smoother for the multigrid algorithm, we conduct a series of numerical experiments to investigate the behavior and efficiency of the multigrid solver in solving the linearized systems, by choosing several preconditioners for the Krylov subspace method. It is shown that the overall efficiency of the damped Newton multigrid algorithm is highly related to the quality of the preconditioner chosen and the number of smoothing steps done on each level. ILU preconditioners based on the Jacobian pattern are found to be robust and provide efficient smoothing but at an expensive cost of storage. It is also demonstrated that the technique of mesh sequencing and multilevel correction scheme provides significant CPU saving for fine grid calculations by limiting the growth of the Krylov iterations.

AB - We employ a damped Newton multigrid algorithm to solve a nonlinear system arising from a finite-difference discretization of an elliptic flame sheet problem. By selecting the generalized minimum residual method as the linear smoother for the multigrid algorithm, we conduct a series of numerical experiments to investigate the behavior and efficiency of the multigrid solver in solving the linearized systems, by choosing several preconditioners for the Krylov subspace method. It is shown that the overall efficiency of the damped Newton multigrid algorithm is highly related to the quality of the preconditioner chosen and the number of smoothing steps done on each level. ILU preconditioners based on the Jacobian pattern are found to be robust and provide efficient smoothing but at an expensive cost of storage. It is also demonstrated that the technique of mesh sequencing and multilevel correction scheme provides significant CPU saving for fine grid calculations by limiting the growth of the Krylov iterations.

KW - ILU preconditioning

KW - Laminar diffusion flame

KW - Newton multigrid algorithm

KW - Nonlinear methods

KW - Vorticity-velocity formulation

UR - http://www.scopus.com/inward/record.url?scp=0141838930&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141838930&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0141838930

VL - 38

SP - 269

EP - 279

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 3-4

ER -