Abstract
We consider time domain electromagnetic scattering from a bounded homogeneous penetrable obstacle. The problem is reduced to a system of time dependent integral equations on the boundary of the scatterer. Using convolution quadrature in time and a Galerkin method on the boundary we derive error estimates for the fully discrete system of boundary integral equations. This is accomplished by proving parameter dependent estimates for the discrete and continuous integral equation system in the Laplace transform domain. In particular a non-standard transmission problem is analyzed. Besides the error estimates, the paper provides a useful extension result and estimates for the spatially semi-discrete problem.
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Bachelot, A., Bounhoure, L., Pujols, A.: Couplage éléments finis-potentiels retardés pour la diffraction électromagnétique par un obstacle hétérogéne. Numer. Math. 89, 257–306 (2001)
Ballani, J., Banjai, L., Sauter, S., Veit, A.: Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge Kutta convolution quadrature. Numer. Math. 123, 643–670 (2013)
Bamberger, A., Duong, T.H.: Formulation variationnelle espace-temps pour le calcul par potentiel retarde de la diffraction d’une onde acoustique (I). Math. Meth. Appl. Sci. 8, 405–435 (1986)
Banjai, L., Sauter, S.: Rapid solution of the wave equation in unbounded domains. SIAM J. Numer. Anal. 47, 227–249 (2008)
Buffa, A., Hiptmair, R., von Petersdorff, T., Schwab, C.: Boundary element methods for Maxwell transmission problems in Lipschitz domains. Numer. Math. 95, 459–485 (2003)
Chen, Q., Monk, P., Weile, D.: Analysis of convolution quadrature applied to the time electric field integral equation. Commun. Comput. Phys. 11, 383–399 (2012)
Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York (2012)
Costabel, M.: Time-dependent problems with the boundary integral equation method. In: Stein, E., de Borst, R., Hughes, T.J.R. (eds.) Encyclopedia of Computational Mechanics. Fundamentals, ch. 25, vol. 1, pp. 703–721. Wiley, New York (2005)
Davies, P.J., Duncan, D.B.: Convolution-in-time approximations of time domain boundary integral equations. SIAM J. Sci. Comput. 35, B43–B61 (2013)
Ha-Duong, T.: On retarded potential boundary integral equations and their discretizations. In: Ainsworth, M. (ed) Topics in Computational Wave Propagation: Direct and Inverse Problems, pp. 301–36. Springer, Berlin (2003)
Hiptmair, R., Schwab, C.: Natural boundary element methods for the electric field integral equation on polyhedra. SIAM J. Numer. Anal. 40, 66–86 (2002)
Laliena, A., Sayas, F.: Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves. Numer. Math. 112, 637–678 (2009)
Lubich, C.: On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Numer. Math. 67, 365–389 (1994)
Nédélec, J.-C.: Acoustic and Electromagnetic Equations, no. 144 in Applied Mathematical Sciences. Springer, New York (2001)
Valdes, F., Ghaffari-Miab, M., Andriulli, F.P., Cools, K., Michielssen, E.: High-order Calderon preconditioned time domain integral equation solvers. IEEE Trans. Antennas Propagat. 61, 2570–2588 (2013)
Wang, X., Weile, D.: Electromagnetic scattering from dispersive dielectric scatterers using the finite difference delay modeling method. IEEE Trans. Antennas Propagat. 58, 1720–1730 (2010)
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Communicated by Ralf Hiptmair.
Research supported in part by AFOSR Grant # FA 9550-11-1-0189 and NSF Grant # DMS-1114889.
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Chan, J.FC., Monk, P. Time dependent electromagnetic scattering by a penetrable obstacle. Bit Numer Math 55, 5–31 (2015). https://doi.org/10.1007/s10543-014-0500-6
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DOI: https://doi.org/10.1007/s10543-014-0500-6