Convex source support in three dimensions

Research output: Scientific - peer-reviewArticle

Details

Original languageEnglish
Pages (from-to)45-63
Number of pages19
JournalBIT Numerical Mathematics
Volume52
Issue number1
StatePublished - Mar 2012
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • Johannes Gutenberg University Mainz

Abstract

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. © 2011 Springer Science + Business Media B.V.

    Research areas

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

ID: 3226996