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Identification of Current Sources in 3D Electrostatics

  • Aron Sommer
  • Andreas Helfrich-Schkarbanenko
  • Vincent Heuveline
Living reference work entry

Abstract

Motivated by passive airborne geoexploration we consider a source identification problem. This problem setting arises in electrostatics and it turns out to be a linear, ill-posed inverse problem. After developing a theoretical framework for corresponding elliptic forward problem, an approach for reconstructing current sources from local electric potential data is illustrated. A pseudo-solution is achieved by means of Tikhonov regularization. The performance of the method is shown by three-dimensional synthetic and real-life numerical examples. For numerical modeling, we choose Method of Finite Elements provided by COMSOL Multiphysics and apply MATLAB for developing a reconstruction algorithm.

Keywords

Inverse Problem Direct Problem Tikhonov Regularization Unique Solvability Forward Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Jörg Bäuerle for his fruitful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aron Sommer
    • 1
  • Andreas Helfrich-Schkarbanenko
    • 2
  • Vincent Heuveline
    • 2
  1. 1.Institut für Informationsverarbeitung (TNT)Leibniz Universität HannoverHannoverGermany
  2. 2.Institute for Applied and Numerical Mathematics 4Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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