Convex source support in three dimensions

Autor: Eva Schweickert, Nuutti Hyvönen, Martin Hanke, Lauri Harhanen
Rok vydání: 2011
Předmět:
Zdroj: BIT Numerical Mathematics. 52:45-63
ISSN: 1572-9125
0006-3835
DOI: 10.1007/s10543-011-0338-0
Popis: 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 Mobius transformations. However, replacing the Mobius 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.
Databáze: OpenAIRE
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