Two methods for discretizing a delta function supported on a level set

Journal of Computational Physics

Volumn 220, Issue 2, 2007, Pages 915-931

  Towers, John D ^a  

^a MiraCosta College   (United States)

Author keywords

Convergence; Delta function; Discretization; Level set method

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MESH GENERATION;

CONVERGENCE; DIRAC DELTA FUNCTION; DISCRETE SETS; DISCRETIZATIONS; LEVEL SET; LEVEL SET METHOD; REGULAR MESHES; SIMPLE++; SMOOTH FUNCTIONS; ZERO LEVEL SET;

DELTA FUNCTIONS;

EID: 33845599106     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.05.037     Document Type: Article

References (12)

1. Beyer R.P., and Leveque R.J. Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Anal. 29 (1992) 332-364
2. B. Engquist, A.K. Tornberg, R. Tsai, Discretization of Dirac Delta Functions in Level Set Methods. Preprint available from: .
3. Osher S., and Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces (2003), Springer-Verlag, New York
4. Osher S., and Sethian J. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12-49
5. Peng D., Merriman B., Osher S., Zhao H., and Kang M. A PDE-based fast local level set method. J. Comput. Phys. 155 (1999) 410-438
6. Peskin C.S. The immersed boundary method. Acta Numerica 11 (2002) 479-511
7. Sethian J.A. Level Set Methods and Fast Marching Methods (1999), Cambridge University Press, Cambridge
8. Smereka P. The numerical approximation of a delta function with application to level set methods. J. Comput. Phys. 211 (2006) 77-90
9. Spivak M. Calculus on Manifolds (1965), W.A. Benjamin, Inc., New York
10. Tornberg A.K., and Engquist B. Numerical approximations of singular source terms in differential equations. J. Comput. Phys. 200 (2004) 462-488
11. Tornberg A.K., and Engquist B. Regularization techniques for numerical approximation of PDEs with singularities. J. Sci. Comput. 19 (2003) 527-552
12. H.K. Zhao, S. Osher, T. Chan, B. Merriman, Variational formulation for motion of multiple junctions and interfaces by level set approach, Preprint available from: .