Delta Function Approximations in Level Set Methods by Distance Function Extension
2010 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, no 6, 2199-2219 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 229, no 6, 2199-2219 p.
Level set method, Delta function, Consistent approximations, Discretization, Distance function
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-10506DOI: 10.1016/j.jcp.2009.11.030ISI: 000275092000015ScopusID: 2-s2.0-73649126152OAI: oai:DiVA.org:kth-10506DiVA: diva2:218471
FunderKnut and Alice Wallenberg Foundation
QC 20100907. Uppdaterat från Manuskript till Artikel (20100907)2009-05-192009-05-192011-05-03Bibliographically approved