Lötstedt, Per and Ramage, Allison and von Sydow, Lina and Söderberg, Stefan (2004) *Preconditioned implicit solution of linear hyperbolic equations with adaptivity.* Journal of Computational and Applied Mathematics, 194 (2). pp. 269-289. ISSN 0377-0427

## Abstract

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.

Item type: | Article |
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ID code: | 2152 |

Keywords: | finite volume method, linear multistep method, adaptivity, semi-toeplitz preconditioning, GMRES, parallel computation, Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 11 Dec 2006 |

Last modified: | 12 Mar 2012 10:37 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2152 |

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