数値解析・応用解析セミナー

7月28日(木) 15:30 -- 17:00  藤原 宏志 (京都大学情報学研究科)
             "Discontinuous Galerkin Approach to the Stationary Radiative
             Transport Equation and Its Applications to Tomography from
             Scattered Signals"

＜研究発表要旨＞
In this talk, we propose a reliable numerical scheme for the stationary
radiative transport equation (RTE) by discontinuous Galerkin methods.
Its applications to numerical experiments on medical imaging are also
shown.
  RTE is a mathematical model of particle migration in turbid media
involved with absorption an scattering, and its analysis plays an
important role in development of medical imaging such as positron
emission tomography or diffused optical tomography. Monte Carlo methods
have been conventionally adopted as standard numerical methods, while
their mathematical reliability has not been established completely.
  Our proposed scheme is obtained by use of the upwind piecewise
continuous approximation. We have established unique existence of
its numerical solution and an error estimate to the proposed scheme.
To show its effectiveness, its application to numerical reconstruction
of the attenuation coefficient of RTE is also shown. This talk is based
on a joint work with Dr. Daisuke Kawagoe (Kyoto University) and
Dr. I-Kun Chen (National Taiwan University).

●セミナー室: 京都大学 総合研究12号館 2階203号
              （応用解析学講座セミナー室）

●総合研究12号館はキャンパスマップでは「京都大学本部構内 54番建物」です。
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セミナー連絡先: 京都大学大学院 情報学研究科 先端数理科学専攻
                 磯 祐介    e-mail; iso at i.kyoto-u.ac.jp