The numerical approximation of a delta function with application to level set methods
The numerical approximation of a delta function with application to level set methods
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DOI：
10.1016/j.jcp.2005.05.005
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发表时间：
2006-01-01
影响因子：
4.1
通讯作者：
Smereka, P
中科院分区：
文献类型：
--
作者：
Smereka, P
它表明，可以使用由Anita马约[泊松方程和不规则区域上的双调和方程的快速解，SIAM J. Sci. Comput. 21（1984）285-299]用于具有不连续源项的椭圆方程的数值解。这个δ函数集中在连续函数的零水平集上。在两个空间维度中，这对应于三个空间维度中的线和面。一阶和二阶精度的Delta函数在两个和三个维度中根据水平集函数来制定。这些delta函数的数值实现达到了预期的精度。(c)2005年爱思唯尔公司All rights reserved.
It is shown that a discrete delta function can be constructed using a technique developed by Anita Mayo [The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Sci. Comput. 21 (1984) 285-299] for the numerical solution of elliptic equations with discontinuous source terms. This delta function is concentrated on the zero level set of a continuous function. In two space dimensions, this corresponds to a line and a surface in three space dimensions. Delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function. The numerical implementation of these delta functions achieves the expected order of accuracy. (c) 2005 Elsevier Inc. All rights reserved.