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MiS Preprint

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

Lehel Banjai


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.

MSC Codes:
65R20, 65L06
Time-domain boundary integral operators, convolution quadrature, Dirichlet-to-Neumann operator

Related publications

2014 Repository Open Access
Lehel Banjai

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

In: IMA journal of numerical analysis, 34 (2014) 3, pp. 1136-1155