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Numerical Analysis Seminar
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
2016/07/11
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroshi Fujiwara (Kyoto University)
Towards fast and reliable numerical computations of the stationary radiative transport equation (日本語)
Hiroshi Fujiwara (Kyoto University)
Towards fast and reliable numerical computations of the stationary radiative transport equation (日本語)
[ Abstract ]
The radiative transport equation (RTE) is a mathematical model of near-infrared light propagation in human tissue, and its analysis is required to develop a new noninvasive monitoring method of our body or brain activities. Since stationary RTE describes light intensity depending on a position and a direction, a discretization model of 3D-RTE is essentially a five dimensional problem. Therefore to establish a reliable and practical numerical method, both theoretical numerical analysis and computing techniques are required.
We firstly introduce huge-scale computation examples of RTE with bio-optical data. A high-accurate numerical cubature on the unit sphere and a hybrid parallel computing technique using GPGPU realize fast computation. Secondly we propose a semi-discrete upwind finite volume method to RTE. We also show its error estimate in two dimensions.
This talk is based on joint works with Prof. Y.Iso, Prof. N.Higashimori, and Prof. N.Oishi (Kyoto University).
The radiative transport equation (RTE) is a mathematical model of near-infrared light propagation in human tissue, and its analysis is required to develop a new noninvasive monitoring method of our body or brain activities. Since stationary RTE describes light intensity depending on a position and a direction, a discretization model of 3D-RTE is essentially a five dimensional problem. Therefore to establish a reliable and practical numerical method, both theoretical numerical analysis and computing techniques are required.
We firstly introduce huge-scale computation examples of RTE with bio-optical data. A high-accurate numerical cubature on the unit sphere and a hybrid parallel computing technique using GPGPU realize fast computation. Secondly we propose a semi-discrete upwind finite volume method to RTE. We also show its error estimate in two dimensions.
This talk is based on joint works with Prof. Y.Iso, Prof. N.Higashimori, and Prof. N.Oishi (Kyoto University).
