Delta function approximations in level set methods by distance function extension

In [A.-K. Tornberg, B. Engquist, Numerical approximations of singular source terms in differential equations, J. Comput. Phys. 200 (2004) 462–488], it was shown for simple examples that the then most common way to regularize delta functions in connection to level set methods produces inconsistent ap...

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Bibliographic Details
Published in:Journal of computational physics 2010-03, Vol.229 (6), p.2199-2219
Main Authors: Zahedi, Sara, Tornberg, Anna-Karin
Format: Article
Language:English
Subjects:
Computational techniques
Consistent approximations
Delta function
Discretization
Distance function
Exact sciences and technology
Information technology
Informationsteknik
Level set method
Mathematical methods in physics
Physics
TECHNOLOGY
TEKNIKVETENSKAP
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Summary:In [A.-K. Tornberg, B. Engquist, Numerical approximations of singular source terms in differential equations, J. Comput. Phys. 200 (2004) 462–488], it was shown for simple examples that the then most common way to regularize delta functions in connection to level set methods produces inconsistent approximations with errors that are not reduced with grid refinement. Since then, several clever approximations have been derived to overcome this problem. However, the great appeal of the old method was its simplicity. In this paper it is shown that the old method – a one-dimensional delta function approximation extended to higher dimensions by a distance function – can be made accurate with a different class of one-dimensional delta function approximations. The prize to pay is a wider support of the resulting delta function approximations.
ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2009.11.030