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Tuesday Seminar of Analysis
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi |
2014/01/21
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nao Hamamuki (Graduate shool of Mathematical Sciences, the University of Tokyo)
An improved level set method based on comparison with a signed distance function (JAPANESE)
Nao Hamamuki (Graduate shool of Mathematical Sciences, the University of Tokyo)
An improved level set method based on comparison with a signed distance function (JAPANESE)
[ Abstract ]
In the classical level set method, a slope of a solution to level set
equations can be close to zero as time develops even if the initial
slope is large, and this prevents one from computing interfaces given as
the level set of the solution. To overcome this issue we introduce an
improved equation by adding an extra term to the original equation.
Then, by applying a comparison principle to the signed distance function
to the interface, we prove that, globally in time, the slope of a
solution of the initial value problem is preserved near the zero level set.
In the classical level set method, a slope of a solution to level set
equations can be close to zero as time develops even if the initial
slope is large, and this prevents one from computing interfaces given as
the level set of the solution. To overcome this issue we introduce an
improved equation by adding an extra term to the original equation.
Then, by applying a comparison principle to the signed distance function
to the interface, we prove that, globally in time, the slope of a
solution of the initial value problem is preserved near the zero level set.
