e & i Elektrotechnik und Informationstechnik

, Volume 124, Issue 7–8, pp 254–259 | Cite as

Boundary integral equation methods for inverse problems in electrical engineering

  • G. Of
  • A. Schwaigkofler
  • O. Steinbach
Originalarbeit
Received:
Accepted:

Summary

Solving inverse problems gets more and more important in the computer simulation of technical processes, as for example in electrical engineering. Here, we present some methods of shape reconstruction from electrical capacitance tomography measurement data. To minimize the cost functional, we need to calculate the corresponding shape derivatives. Fast boundary element methods are used for solving the appropriate forward problems to reduce the quadratic effort to an almost linear one.

Keywords

Inverse problems Shape derivatives Boundary integral equations Fast boundary element methods 

Randintegralmethoden zur Lösung inverser Probleme in der Elektrotechnik

Zusammenfassung

Die Lösung inverser Probleme spielt eine immer wichtigere Rolle in der Computersimulation technischer Vorgänge, so auch in der Elektrotechnik. In diesem Beitrag werden einige Lösungsansätze zur Gebietsrekonstruktion aus ermittelten Messdaten der elektrischen Kapazitätstomografie dargestellt. Die Minimierung des Kostenfunktionals erfordert die Berechnung entsprechender Gebietsableitungen. Zur Lösung der zugehörigen Vorwärtsprobleme werden hier schnelle Randelementmethoden eingesetzt, die den sonst quadratischen Aufwand auf ein fast lineares Verhalten reduzieren.

Schlüsselwörter

Inverse Probleme Gebietsableitungen Randintegralmethoden Schnelle Randelementmethoden 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • G. Of
    • 1
  • A. Schwaigkofler
    • 1
  • O. Steinbach
    • 1
  1. 1.Institute of Computational MathematicsGraz University of TechnologyGrazAustria

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