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Identification of Current Sources in 3D Electrostatics

In: Handbook of Geomathematics

Author

Listed:
  • Aron Sommer

    (Leibniz Universität Hannover, Institut für Informationsverarbeitung (TNT))

  • Andreas Helfrich-Schkarbanenko

    (Karlsruhe Institute of Technology (KIT), Institute for Applied and Numerical Mathematics)

  • Vincent Heuveline

    (Karlsruhe Institute of Technology, Engineering Mathematics and Computing Lab (EMCL)
    Karlsruhe Institute of Technology (KIT), Institute for Applied and Numerical Mathematics
    Engineering Mathematics and Computing Lab, University of Heidelberg, Interdisciplinary Center for Scientific Computing)

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.

Suggested Citation

  • Aron Sommer & Andreas Helfrich-Schkarbanenko & Vincent Heuveline, 2015. "Identification of Current Sources in 3D Electrostatics," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 1863-1885, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_85
    DOI: 10.1007/978-3-642-54551-1_85
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