Time-domain Dirichlet-to-Neumann map and its discretization
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Submission date: 16. Jan. 2012 (revised version: February 2012)
published in: IMA journal of numerical analysis, 34 (2014) 3, p. 1136-1155
DOI number (of the published article): 10.1093/imanum/drt032
MSC-Numbers: 65R20, 65L06
Keywords and phrases: Time-domain boundary integral operators, convolution quadrature, Dirichlet-to-Neumann operator
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In this work we address 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 scaterrer, and the type of convolution quadrature used (linear multistep or Runge-Kutta) and its convergence order.