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

  • Authors:

  • Peter Smereka

  • Affiliations:

  • Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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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.