Extrinsic meshfree approximation using asymptotic expansion for interfacial discontinuity of derivative

Do Wan Kim, Young Cheol Yoon, Wing Kam Liu*, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A sharp meshfree approximation for derivative discontinuities across arbitrary interfaces is proposed. The interface can be arbitrarily located in a domain in which nodes are distributed uniformly or irregularly. The proposed meshfree approximations consist of two parts, singular and regular. The moving least square meshfree approximation is used together with the local wedge function as basis functions. The approximations for discontinuities are applied in a meshfree point collocation method to obtain solutions of the Poisson problem with a layer delta source on the interface and second order elliptic problems with discontinuous coefficients and/or the singular layer sources along the interface. The numerical calculations show that this method has good performance even on irregular node models.

Original languageEnglish (US)
Pages (from-to)370-394
Number of pages25
JournalJournal of Computational Physics
Issue number1
StatePublished - Jan 20 2007


  • Arbitrary interface
  • Discontinuous coefficients
  • Elliptic problem
  • Extrinsic meshfree approximation
  • Local wedge function
  • Meshfree point collocation method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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