The inverse problem of dipolar source identification from incomplete boundary measurements. (English) Zbl 1539.35293
Summary: We consider and combine two methods to solve the inverse problem of locating dipolar sources in a restricted domain from measurements of the Cauchy data on a part of the boundary for the Laplace equation. We begin by extending the boundary measurements, which are accessible only on a part of the boundary by solving an extremal bounded problem in an annulus. The inverse problem of source identification is then solved using the reciprocity gap concept applied to the completed data. In order to evaluate the effectiveness of source detection with regard to the expansion of the data, some numerical tests are provided.
© 2023 John Wiley & Sons, Ltd.
© 2023 John Wiley & Sons, Ltd.
MSC:
| 35R30 | Inverse problems for PDEs |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
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