Convex source support in three dimensions

Martin Hanke, Lauri Harhanen, Nuutti Hyvönen*, Eva Schweickert

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


This work extends the algorithm for computing the convex source support in the framework of the Poisson equation to a bounded three-dimensional domain. The convex source support is, in essence, the smallest (nonempty) convex set that supports a source that produces the measured (nontrivial) data on the boundary of the object. In particular, it belongs to the convex hull of the support of any source that is compatible with the measurements. The original algorithm for reconstructing the convex source support is inherently two-dimensional as it utilizes Möbius transformations. However, replacing the Möbius transformations by inversions with respect to suitable spheres and introducing the corresponding Kelvin transforms, the basic ideas of the algorithm carry over to three spatial dimensions. The performance of the resulting numerical algorithm is analyzed both for the inverse source problem and for electrical impedance tomography with a single pair of boundary current and potential as the measurement data.

Original languageEnglish
Pages (from-to)45-63
Number of pages19
JournalBIT Numerical Mathematics
Issue number1
Publication statusPublished - Mar 2012
MoE publication typeA1 Journal article-refereed


  • Convex source support
  • Electrical impedance tomography
  • Inverse elliptic boundary value problem
  • Obstacle problem


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