## A PDE-based fast local level set method.(English)Zbl 0964.76069

From the summary: We develop a fast method to localize the level set method of S. Osher and J. A. Sethian [ibid. 79, No. 1, 12-49 (1988; Zbl 0659.65132)], and address two important issues that are intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface. This fast local level set method reduces the computational effort by one order of magnitude, works in as much generality as the original one, and is conceptually simple and easy to implement.
Our approach differs from previous related works in that we extract all the information needed from the level set function (or functions in multiphase flow) and do not need to find explicitly the location of the interface in the space domain. The complexity of our method to do tasks such as extension and distance reinitialization is $$O(N)$$, where $$N$$ is the number of points in space, not $$O(N\log N)$$. This complexity estimation is also valid for quite general geometrically based front motion for our localized method.

### MSC:

 76M25 Other numerical methods (fluid mechanics) (MSC2010)

Zbl 0659.65132
Full Text:

### References:

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