Discretizing delta functions via finite differences and gradient normalization

  • Authors:

  • John D. Towers

  • Affiliations:

  • MiraCosta College, 3333 Manchester Avenue, Cardiff-by-the-Sea, CA 92007-1516, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

In [J.D. Towers, Two methods for discretizing a delta function supported on a level set, J. Comput. Phys. 220 (2007) 915-931] the author presented two closely related finite difference methods (referred to here as FDM1 and FDM2) for discretizing a delta function supported on a manifold of codimension one defined by the zero level set of a smooth mapping u:R^n@?R. These methods were shown to be consistent (meaning that they converge to the true solution as the mesh size h-0) in the codimension one setting. In this paper, we concentrate on n=:R^n@?R^m,1=