caa a22 4500 378921428 CHVBK 20180305123606.0 cr unu---uuuuu 161128e20041201xx s 000 0 eng 10.1515/1569394042545111 doi (NATIONALLICENCE)gruyter-10.1515/1569394042545111 Two approaches to the problem of defect correction in vector field tomography solving boundary value problems [Elektronische Daten] [E. Yu. Derevtsov, A. K. Louis, T. Schuster] 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. Copyright 2004, Walter de Gruyter Derevtsov E. Yu Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090. E-mail: dert@math.nsc.ru aut Louis A. K. Fachrichtung Mathematik, Geb. 36.1, Universität des Saarlandes, 66041 Saarbrücken, Germany. E-mails: louis@num.uni-sb.de, derevtsov@num.uni-sb.de aut Schuster T. Department of Mathematics, Tufts University, Medford, MA 02155, USA. E-mail: thomas.schuster@tufts.edu aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/6(2004-12-01), 597-626 0928-0219 12:6<597 2004 12 jiip https://doi.org/10.1515/1569394042545111 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569394042545111 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Derevtsov E. Yu Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090. E-mail: dert@math.nsc.ru aut NATIONALLICENCE 700 1- Louis A. K. Fachrichtung Mathematik, Geb. 36.1, Universität des Saarlandes, 66041 Saarbrücken, Germany. E-mails: louis@num.uni-sb.de, derevtsov@num.uni-sb.de aut NATIONALLICENCE 700 1- Schuster T. Department of Mathematics, Tufts University, Medford, MA 02155, USA. E-mail: thomas.schuster@tufts.edu aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/6(2004-12-01), 597-626 0928-0219 12:6<597 2004 12 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter