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

25 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 Jan 1

Fingerprint

Meshfree
Interface Problems
Wedge
Collocation Method
Basis Functions
Moving Least-squares Approximation
Curved Boundary
Derivative
Meshfree Method
Least squares approximations
Derivatives
Shape Function
Straight
Numerical Scheme
Interfaces (computer)
Asymptotic Behavior
Robustness
Numerical Results
Polynomials
Polynomial

All Science Journal Classification (ASJC) codes

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

Cite this

Kim, Do Wan ; Liu, Wing Kam ; Yoon, Young Cheol ; Belytschko, Ted ; Lee, Sang-Ho. / Meshfree point collocation method with intrinsic enrichment for interface problems. In: Computational Mechanics. 2007 ; Vol. 40, No. 6. pp. 1037-1052.
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Meshfree point collocation method with intrinsic enrichment for interface problems. / Kim, Do Wan; Liu, Wing Kam; Yoon, Young Cheol; Belytschko, Ted; Lee, Sang-Ho.

In: Computational Mechanics, Vol. 40, No. 6, 01.01.2007, p. 1037-1052.

Research output: Contribution to journalArticle

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