Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations
Numerical Analysis
2020-09-03 v3 Numerical Analysis
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.
Cite
@article{arxiv.1911.02806,
title = {Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations},
author = {Marion Darbas and Jérémy Heleine and Stephanie Lohrengel},
journal= {arXiv preprint arXiv:1911.02806},
year = {2020}
}