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Advanced Methods for Computational Electromagnetics

Research Project
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01.10.2008
 - 30.09.2010

Computational electromagnetics (CEM) presents a number of challenges. First, electromagnetic fields tend to be highly {em oscillatory} and {em wave-dominated}; moreover, they can develop {em singularities} at material interfaces and boundaries. Second, the phenomena of interest typically involve {em complicated} geometries, {em multi-physics}, {em inhomogeneous} media, and even {em nonlinear} materials. Third, the underlying partial differential equations often need to be solved in an unbounded domain, which needs to be truncated by an {em artificial boundary} to confine the region of interest to a finite computational domain. Fourth, standard preconditioners are typically ineffective for the highly indefinite ill-conditioned sparse linear systems of equations that appear in higher frequency regimes. Computational electromagnetics (CEM) presents a number of challenges. First,electromagnetic fields tend to be highly oscillatory and wave-dominated; moreover, they can develop singularities at material interfaces and boundaries. Second, the phenomena of interest typically involve complicated geometries, multi-physics, inhomogeneous media, and even nonlinear materials.Third, the underlying partial differential equations often need to be solved in an unbounded domain, which needs to be truncated by an artificial boundary to confine theregion of interest to a finite computational domain.

Publications

Diaz, Julien and Grote, Marcus J. (2009) ‘Energy conserving explicit local time-stepping for second-order wave equations’, SIAM journal on scientific computing, 31(3), pp. 1985–2014. Available at: https://doi.org/10.1137/070709414.

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Grote, Marcus J. and Schoetzau, Dominik (2009) ‘Optimal error estimates for the fully discrete interior penalty DG method for the wave equation’, Journal of scientific computing, 40(1-3), pp. 257–272. Available at: https://doi.org/10.1007/s10915-008-9247-z.

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Grote, Marcus J. and Sim, Imbo (2009) ‘On local nonreflecting boundary conditions for time-dependent wave propagation’, Chinese annals of mathematics. Ser. B, 30(5), pp. 589–606. Available at: https://doi.org/10.1007/s11401-009-0203-5.

URLs
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Grote, M. and Mitkova, T. (2009) ‘Explicit local time-stepping for transient electromagnetic waves’, in Barucq, H.; Bonnet-Bendhia, A.-S.; Cohen, G.; Diaz, J.; Ezziani, A.; Joly, P. (ed.). INRIA: INRIA.

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Members (2)

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Marcus J. Grote

Principal Investigator
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Teodora Mitkova

Project Member