Sparsity of Runge-Kutta convolution weights for the three-dimensional wave equation

Lehel Banjai, Maryna Kachanovska

Research output: Contribution to journalArticle

Abstract

Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge-Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for the assembly of the fully discrete systems.

Original languageEnglish
Pages (from-to)901-936
Number of pages36
JournalBIT Numerical Mathematics
Volume54
Issue number4
Early online date17 Jun 2014
DOIs
Publication statusPublished - Dec 2014

Fingerprint

Runge-Kutta
Wave equations
Convolution
Sparsity
Quadrature
Wave propagation
Integral equations
Wave equation
Three-dimensional
Discrete Systems
Galerkin
Wave Propagation
Fast Algorithm
Time Domain
Integral Equations
Discretization

Keywords

  • Convolution quadrature
  • Runge-Kutta methods
  • Time-domain boundary integral equations
  • Wave equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Software
  • Computer Networks and Communications

Cite this

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abstract = "Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge-Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for the assembly of the fully discrete systems.",
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Sparsity of Runge-Kutta convolution weights for the three-dimensional wave equation. / Banjai, Lehel; Kachanovska, Maryna.

In: BIT Numerical Mathematics, Vol. 54, No. 4, 12.2014, p. 901-936.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Banjai, Lehel

AU - Kachanovska, Maryna

PY - 2014/12

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AB - Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge-Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for the assembly of the fully discrete systems.

KW - Convolution quadrature

KW - Runge-Kutta methods

KW - Time-domain boundary integral equations

KW - Wave equation

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DO - 10.1007/s10543-014-0498-9

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SN - 0006-3835

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