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arXiv · 1911.02806

Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations

Marion Darbas·Jérémy Heleine·Stephanie Lohrengel
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Abstract

This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain from measured data on the accessible part. The non-iterative quasi-reversibility method is studied and different mixed variational formulations are proposed. Well-posedness, convergence and regularity results are proved. Discretization is performed by means of edge finite elements. Various two- and three-dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.

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Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. 2019-11-07. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. https://arxiv.org/abs/1911.02806

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