Preconditioned implicit solution of linear hyperbolic equations with adaptivity

Per Lötstedt, Allison Ramage, Lina von Sydow, Stefan Söderberg

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.
Original languageEnglish
Pages (from-to)269-289
Number of pages20
JournalJournal of Computational and Applied Mathematics
Issue number2
Publication statusPublished - Sept 2004


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


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