Convex source support in three dimensions

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

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

5 Sitaatiot (Scopus)

Abstrakti

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.

AlkuperäiskieliEnglanti
Sivut45-63
Sivumäärä19
JulkaisuBIT Numerical Mathematics
Vuosikerta52
Numero1
DOI - pysyväislinkit
TilaJulkaistu - maaliskuuta 2012
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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