Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
IMPACT FACTOR 2017: 0.941
5-year IMPACT FACTOR: 0.953
CiteScore 2017: 0.91
SCImago Journal Rank (SJR) 2017: 0.461
Source Normalized Impact per Paper (SNIP) 2017: 1.022
Mathematical Citation Quotient (MCQ) 2017: 0.49
Two approaches to the problem of defect correction in vector field tomography solving boundary value problems
- Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090. E-mail:
- Fachrichtung Mathematik, Geb. 36.1, Universität des Saarlandes, 66041 Saarbrücken, Germany. E-mails: ,
- Other articles by this author:
- De Gruyter OnlineGoogle Scholar
The problem of vector field tomography consists of reconstructing a vector field from integrals of certain projections of the field over geodesic lines. In case of an homogeneous medium the underlying Riemannian metric is the Euclidean one and the geodesics are straight lines. Modeling inhomogeneous media we take also non-Euclidean metrics into account. It is well known that the corresponding integral transform has a nontrivial kernel consisting of potential fields with potentials being equal to a constant on the boundary of the domain. Thus, the reconstruction from these data may contain a potential part of this type. Since we consider only solenoidal fields, e.g.velocity fields of incompressible fluids, the accuracy of the solution can be improved detecting the undesirable potential part of the reconstruction and subtracting it. Depending on the boundary condition the sought potential is the solution of either a Dirichlet or a Neumann boundary value problem. In this article two approaches to recover the potential are suggested: One deals with the solution of the Dirichlet problem with a finite difference scheme, the other solves the Neumann problem with the help of boundary element methods.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.