Date of Award

Spring 2006

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics & Statistics


Computational and Applied Mathematics

Committee Director

David E. Keyes

Committee Member

Hideaki Kaneko

Committee Member

Fang Q. Hu

Committee Member

Glenn Williams

Committee Member

Alexander L. Godunov


The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily determined from the level set function &phis;. There are many applications of the level set method, including kinetic crystal growth, epitaxial growth of thin films, image restoration, vortex dominated flows, and so forth. Most applications described in the growing literature on the applications of level sets advance the level set equation with explicit time integration. Hence, small CFL-respecting time steps are needed to maintain stability. In this thesis, an implicit level set method is introduced and applied to wildland firespread models, removing vulnerability to instability.


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