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

2019/11/07 by Marion Darbas, Darbas, Marion, Jérémy Heleine +3
Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.1911.02806

openalex publication_date 2019/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Limitations of the L-curve method in ill-posed problems
• Mixed finite elements in ?3
• A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation

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