A PDE-based fast local level set method
A PDE-based fast local level set method
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DOI：
10.1006/jcph.1999.6345
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发表时间：
1999-11-01
影响因子：
4.1
通讯作者：
Kang, MJ
中科院分区：
文献类型：
--
作者：
Peng, DP;Merriman, B;Kang, MJ
我们开发了一种快速方法来本地化Osher和Sethian（1988，J. Comput.物理79，12），并解决两个重要的问题，是固有的水平集方法：（a）如何扩展的量，只在界面上的界面附近;（B）如何重置水平集函数是一个有符号的距离函数的界面有效地没有明显移动的界面。这种快速的局部水平集方法减少了一个数量级的计算工作量，在尽可能多的通用性，因为原来的一个，是概念简单，易于实现。我们的方法不同于以前的相关工作，我们提取的所有信息需要从水平集函数（或功能在多相流），并不需要明确地找到在空间域中的接口的位置。我们的方法的复杂性做任务，如扩展和距离重新初始化是O（N），其中N是空间中的点的数量，而不是O（N log N）的作品由Sethian（1996年，Proc. Not. Acad. Sci. 93，1591）和Helmsen及其同事（1996，SPIE Microlithography IX，第253页）。对于我们的局部化方法，这种复杂性估计对于相当一般的基于几何的前运动也是有效的。(C)北京：科学出版社.
We develop a fast method to localize the level set method of Osher and Sethian (1988, J. Comput. Phys. 79, 12) 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) as in works by Sethian (1996, Proc. Not. Acad. Sci. 93, 1591) and Helmsen and co-workers (1996, SPIE Microlithography IX, p. 253). This complexity estimation is also valid for quite general geometrically based front motion for our localized method. (C) 1999 Academic Press.