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Fast Convolution Quadrature Based Impedance Boundary Conditions

by R. Hiptmair and M. Lopez-Fernandez and A. Paganini

(Report number 2013-02)

Abstract
We consider an eddy current problem in time-domain relying on impedance boundary conditions on the surface of the conductor(s). We pursue its full discretization comprising (i) a finite element Galerkin discretization by means of lowest order edge elements in space, and (ii) temporal discretization based on Runge-Kutta convolution quadrature (CQ) for the resulting Volterra integral equation in time. The final algorithm also involves the fast and oblivious approximation of CQ. For this method we give a comprehensive convergence analysis and establish that the errors of spatial discretization, CQ and of its approximate realization add up to the final error bound.

Keywords: Eddy current problem, impedance boundary conditions, convolution quadrature, fast and oblivious algorithms

@Techreport{HLP13_498,
  author = {R. Hiptmair and M. Lopez-Fernandez and A. Paganini},
  title = {Fast Convolution Quadrature Based Impedance Boundary Conditions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-02.pdf },
  year = {2013}
}

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