| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 85 === This is an analysis of front propagation in infinite domain, includes theory
developement and numerical computation. The forms of front considered here are
closed curves on 2 dimension plane and closed surfaces in 3 dimension space.
There are two representations of position vector of any point on the front:
the parametric equation and the implicit equation. A general front propagation
equation can be derived via the former, the corrseponding numerical method is
front tracking method. It finds out positions of all points on the front, can
descirbe the local behavior of front propagation accurately, but too depends on
the local properties of fronts thus difficulties occurred unavoidably at local
singularity, and can't handle global property change which may occur during
the propagation of fronts. Another front propagation equation is derived via
the relationship of the two representations, the corresponding numerical method
is the level set method. It capatures the position of the front from a scalar
field defined in the whole space.Direct handling of local
singularity is avoided
, and can handle the global property change easily. But it required more
computation resources, and also induced some other singularity
thus difficulties
occurred. This problem origionates from research upon some
physical phenonmena,
but also heavily discuissed in research of pure mathematics. Here discuissed
methods to describe fronts, derived the front propagation equations, and
phenomena occurred while the front is propagating, and showed numerical
computations on 2 and 3 dimension space for both front tracking method and the
level set method.
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