Minimal-norm RKHS solution of an integral model in geo-electromagnetism

In this paper, a numerical method is developed for approximating the solution of a linear integral model in a reproducing kernel Hilbert space (RKHS). The model is typical of frequency domain electromagnetic (FDEM) induction methods in applied geophysics. The original problem is reformulated as a ne...

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Bibliographic Details
Published in2021 21st International Conference on Computational Science and Its Applications (ICCSA) pp. 21 - 28
Main Authors de Alba, Patricia Diaz, Fermo, Luisa, Pes, Federica, Rodriguez, Giuseppe
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2021
Subjects
Computational modeling
Fredholm integral equations of the first kind
frequency domain electromagnetics
Frequency-domain analysis
Geophysics
Hilbert space
Integral equations
inverse problems
Mathematical models
minimal-norm solution
reproducing kernel Hilbert space
Scientific computing
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Summary:In this paper, a numerical method is developed for approximating the solution of a linear integral model in a reproducing kernel Hilbert space (RKHS). The model is typical of frequency domain electromagnetic (FDEM) induction methods in applied geophysics. The original problem is reformulated as a new one whose solution has the same smoothness properties as the original one. Then, the minimal-norm solution of such a model is computed through a numerical method that combines Riesz's theory with regularization tools. Several numerical tests illustrate the performance of the proposed approach.
DOI:10.1109/ICCSA54496.2021.00014