The numerical approximation of a delta function with application to level set methods

@article{citeulike:2151519, abstract = {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.}, author = {Smereka, Peter }, citeulike-article-id = {2151519}, doi = {http://dx.doi.org/10.1016/j.jcp.2005.05.005}, journal = {Journal of Computational Physics}, keywords = {mathematics}, month = {January}, number = {1}, pages = {77--90}, posted-at = {2007-12-20 12:41:28}, priority = {0}, title = {The numerical approximation of a delta function with application to level set methods}, url = {http://dx.doi.org/10.1016/j.jcp.2005.05.005}, volume = {211}, year = {2006} }

TY - JOUR ID - citeulike:2151519 L3 - citeulike-article-id:2151519 TI - The numerical approximation of a delta function with application to level set methods JF - Journal of Computational Physics VL - 211 IS - 1 SP - 77 EP - 90 N2 - 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. KW - mathematics AU - Smereka, Peter PY - 2006/01/01/ UR - http://dx.doi.org/10.1016/j.jcp.2005.05.005 ER -