### Abstract

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

Pages (from-to) | 269-289 |

Number of pages | 20 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 194 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 2004 |

### Fingerprint

### Keywords

- finite volume method
- linear multistep method
- adaptivity
- semi-toeplitz preconditioning
- GMRES
- parallel computation

### Cite this

*Journal of Computational and Applied Mathematics*,

*194*(2), 269-289. https://doi.org/10.1016/j.cam.2004.01.041

}

*Journal of Computational and Applied Mathematics*, vol. 194, no. 2, pp. 269-289. https://doi.org/10.1016/j.cam.2004.01.041

**Preconditioned implicit solution of linear hyperbolic equations with adaptivity.** / Lötstedt, Per; Ramage, Allison; von Sydow, Lina; Söderberg, Stefan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Preconditioned implicit solution of linear hyperbolic equations with adaptivity

AU - Lötstedt, Per

AU - Ramage, Allison

AU - von Sydow, Lina

AU - Söderberg, Stefan

PY - 2004/9

Y1 - 2004/9

N2 - This paper describes a method for solving hyperbolic partial differential equations using an adaptive grid: the spatial derivatives are discretised with a finite volume method on a grid which is structured and partitioned into blocks which may be refined and derefined as the solution evolves. The solution is advanced in time via a backward differentiation formula. The discretisation used is second-order accurate and stable on Cartesian grids. The resulting system of linear equations is solved by GMRES at every time-step with the convergence of the iteration being accelerated by a semi-Toeplitz preconditioner. The efficiency of this preconditioning technique is analysed and numerical experiments are presented which illustrate the behaviour of the method on a parallel computer.

AB - This paper describes a method for solving hyperbolic partial differential equations using an adaptive grid: the spatial derivatives are discretised with a finite volume method on a grid which is structured and partitioned into blocks which may be refined and derefined as the solution evolves. The solution is advanced in time via a backward differentiation formula. The discretisation used is second-order accurate and stable on Cartesian grids. The resulting system of linear equations is solved by GMRES at every time-step with the convergence of the iteration being accelerated by a semi-Toeplitz preconditioner. The efficiency of this preconditioning technique is analysed and numerical experiments are presented which illustrate the behaviour of the method on a parallel computer.

KW - finite volume method

KW - linear multistep method

KW - adaptivity

KW - semi-toeplitz preconditioning

KW - GMRES

KW - parallel computation

UR - http://dx.doi.org/10.1016/j.cam.2004.01.041

U2 - 10.1016/j.cam.2004.01.041

DO - 10.1016/j.cam.2004.01.041

M3 - Article

VL - 194

SP - 269

EP - 289

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -