Preconditioned implicit solution of linear hyperbolic equations with adaptivity

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

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)269-289
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume194
Issue number2
DOIs
Publication statusPublished - Sep 2004

Fingerprint

Linear Hyperbolic Equation
Adaptivity
Backward Differentiation Formula
Preconditioning Techniques
Cartesian Grid
Adaptive Grid
Hyperbolic Partial Differential Equations
GMRES
Otto Toeplitz
Finite volume method
Parallel Computers
System of Linear Equations
Finite Volume Method
Linear equations
Preconditioner
Partial differential equations
Discretization
Numerical Experiment
Grid
Derivatives

Keywords

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

Cite this

Lötstedt, Per ; Ramage, Allison ; von Sydow, Lina ; Söderberg, Stefan. / Preconditioned implicit solution of linear hyperbolic equations with adaptivity. In: Journal of Computational and Applied Mathematics. 2004 ; Vol. 194, No. 2. pp. 269-289.
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Preconditioned implicit solution of linear hyperbolic equations with adaptivity. / Lötstedt, Per; Ramage, Allison; von Sydow, Lina; Söderberg, Stefan.

In: Journal of Computational and Applied Mathematics, Vol. 194, No. 2, 09.2004, p. 269-289.

Research output: Contribution to journalArticle

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