Meshfree point collocation method with intrinsic enrichment for interface problems

Do Wan Kim, Wing Kam Liu, Young Cheol Yoon, Ted Belytschko, Sang Ho Lee

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

A meshfree collocation method with an intrinsic wedge enrichment is presented for solving interface problems. To approximate the class of functions with discontinuous derivatives on the interface, the wedge is asymptotically added to the basis functions. A general class of wedge basis functions with specified orders of asymptotic behavior at the interface is developed for moving least square approximations. These are implemented in diffuse derivative methods where the shape functions are approximately differentiated. The reproducing properties of these approximations for the polynomial part and for the wedge function along straight boundaries of the basis are demonstrated. For curved boundaries, the reproducing properties of the wedge functions are more restricted. Numerical results show the ease of constructing the intrinsic enrichment and the robustness of the numerical scheme in solving interface problems.

Original languageEnglish
Pages (from-to)1037-1052
Number of pages16
JournalComputational Mechanics
Volume40
Issue number6
DOIs
Publication statusPublished - 2007 Nov

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Meshfree point collocation method with intrinsic enrichment for interface problems'. Together they form a unique fingerprint.

  • Cite this