Level Set Algorithm And Its Application

Level set method was developed from fronts propagating. It is a kind of numerical techniques for tracking the evolution of interfaces.This paper presented a new local level set method for monotonically advancing fronts. The local level set method was applied to solve fronts propagating problems and structural topology optimization problems.Traditional level set methods rely on computing the evolution of all the level sets, not simply the zero level set corresponding to the fronts itself. As an alternative, an efficient modification is to perform work only in a neighborhood of the zero level set. As mentioned above, it is not a computationally expensive technique. Our approach is partial differential equation (PDE) based, in the sense that our localization of computation domain, velocity extension, and reinitialization of level set function are all based on solving different PDEs. This leads to a simple, accurate, and flexible method. Our localization works as well as the original method and all of its recent variants do, but require less computing effort. The complexity of our method for the works, such as extension and distance reinitialization, is decreased. This complexity estimation is also valid for quite general geometrically based front motion for our localized method.