Time-domain Dirichlet-to-Neumann map and its discretization

Research output: Contribution to journalArticle

Abstract

In this work we consider the wave equation in homogeneous, unbounded domains and its numerical solution. In particular, we are interested in the effect that the shape of a bounded obstacle has on the quality of some numerical schemes for the computation of the exterior Dirichlet-to-Neumann map. We discretize the Dirichlet-to-Neumann map in time by convolution quadrature and investigate how the correct choice of time step depends on the highest frequency present in the system, the shape of the scatterer and the type of convolution quadrature used (linear multistep or Runge-Kutta) and its convergence order.

Original languageEnglish
Pages (from-to)1136-1155
Number of pages20
JournalIMA Journal of Numerical Analysis
Volume34
Issue number3
DOIs
Publication statusPublished - Jul 2014

Keywords

  • time-domain Dirichlet-to-Neumann operator
  • convolution quadrature
  • linear multistep and Runge-Kutta methods
  • BOUNDARY INTEGRAL-OPERATORS
  • CONVOLUTION QUADRATURE
  • CONDITION NUMBER
  • OPERATIONAL CALCULUS
  • ACOUSTIC SCATTERING
  • NUMERICAL-SOLUTION
  • BEM
  • MULTISTEP
  • EQUATIONS

Cite this

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title = "Time-domain Dirichlet-to-Neumann map and its discretization",
abstract = "In this work we consider the wave equation in homogeneous, unbounded domains and its numerical solution. In particular, we are interested in the effect that the shape of a bounded obstacle has on the quality of some numerical schemes for the computation of the exterior Dirichlet-to-Neumann map. We discretize the Dirichlet-to-Neumann map in time by convolution quadrature and investigate how the correct choice of time step depends on the highest frequency present in the system, the shape of the scatterer and the type of convolution quadrature used (linear multistep or Runge-Kutta) and its convergence order.",
keywords = "time-domain Dirichlet-to-Neumann operator, convolution quadrature, linear multistep and Runge-Kutta methods, BOUNDARY INTEGRAL-OPERATORS, CONVOLUTION QUADRATURE, CONDITION NUMBER, OPERATIONAL CALCULUS, ACOUSTIC SCATTERING, NUMERICAL-SOLUTION, BEM, MULTISTEP, EQUATIONS",
author = "Lehel Banjai",
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doi = "10.1093/imanum/drt032",
language = "English",
volume = "34",
pages = "1136--1155",
journal = "IMA Journal of Numerical Analysis",
issn = "0272-4979",
publisher = "Oxford University Press",
number = "3",

}

Time-domain Dirichlet-to-Neumann map and its discretization. / Banjai, Lehel.

In: IMA Journal of Numerical Analysis, Vol. 34, No. 3, 07.2014, p. 1136-1155.

Research output: Contribution to journalArticle

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KW - NUMERICAL-SOLUTION

KW - BEM

KW - MULTISTEP

KW - EQUATIONS

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