High order numerical methods to a type of delta function integrals

  • Authors:

  • Xin Wen

  • Affiliations:

  • Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

We study second to fourth order numerical methods to a type of delta function integrals in one to three dimensions. These delta function integrals arise from recent efficient level set methods for computing the multivalued solutions of nonlinear PDEs. We show that the natural quadrature approach with usual discrete delta functions and support size formulas to the two dimensional delta function integrals suffer from nonconvergence. We then design high order numerical methods to this type of delta function integrals based on interpolation approach. Numerical examples are presented to verify the efficiency and accuracy of our methods.