Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations
| Autor: | Stephanie Lohrengel, Marion Darbas, Jérémy Heleine |
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| Rok vydání: | 2020 |
| Předmět: |
Cauchy problem
Control and Optimization Discretization Boundary (topology) Numerical Analysis (math.NA) Inverse problem Missing data Finite element method symbols.namesake Maxwell's equations Modeling and Simulation Bounded function FOS: Mathematics symbols Discrete Mathematics and Combinatorics Applied mathematics Pharmacology (medical) Mathematics - Numerical Analysis Analysis Mathematics |
| Zdroj: | Inverse Problems & Imaging. 14:1107-1133 |
| ISSN: | 1930-8345 |
| DOI: | 10.3934/ipi.2020056 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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