Convergence studies for an adaptive meshless least-squares collocation method

Ka Chun Cheung, Leevan LING

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we apply the recently proposed fast block-greedy algorithm to a convergent kernel-based collocation method. In particular, we discretize three-dimensional second-order elliptic differential equations by the meshless asymmetric collocation method with over-sampling. Approximated solutions are obtained by solving the resulting weighted least squares problem. Such formulation has been proven to have optimal convergence in H2. Our aim is to investigate the convergence behaviour of some three dimensional test problems. We also study the low-rank solution by restricting the approximation in some smaller trial subspaces. A block-greedy algorithm, which costs at most O(NK2) to select K columns (or trial centers) out of an M × N overdetermined matrix, is employed for such an adaptivity. Numerical simulations are provided to justify these reductions.

Original languageEnglish
Pages (from-to)377-386
Number of pages10
JournalInternational Journal of Computational Methods and Experimental Measurements
Volume5
Issue number3
DOIs
Publication statusPublished - 2017

Scopus Subject Areas

  • Computational Mechanics
  • Modelling and Simulation
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive greedy algorithm
  • Ansa method
  • Elliptic equation
  • Kernel-based collocation

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