Interaction and multiscale mechanics

  • 제2권3호
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  • Pages.295-319
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  • 2009
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A study on convergence and complexity of reproducing kernel collocation method

  • Hu, Hsin-Yun (Department of Mathematics, Tunghai University) ;
  • Lai, Chiu-Kai (Department of Mathematics, Tunghai University) ;
  • Chen, Jiun-Shyan (Department of Civil and Environmental Engineering, University of California)
  • 투고 : 2009.06.01
  • 심사 : 2009.08.14
  • 발행 : 2009.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, we discuss a reproducing kernel collocation method (RKCM) for solving $2^{nd}$ order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

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