演講公告

新聞標題：　( 2008-11-21 )

• 演講主題：Galerkin and Collocation Meshfree Methods: From Continuum to Quantum

• 主講人：陳俊賢教授(Chancellor's Professor of UCLA)

• 演講日期：97年11月25日(星期二)<br>下午2:00-3:00

• 演講地點：(光復校區)科學一館223室

• 茶會時間：當天下午3:00於科學一館205室

• 摘要內容：
  

  Meshfree methods can be collectively classified into Galerkin type and collocation type. Galerkin type formulation in conjunction with approximation functions with polynomial reproducibility yields algebraic convergence. Through three classes of problems at continuum macro-scale, meso-scale, and quantum-scale, we demonstrate the convergence properties of Galerkin meshfree approach and how it can be constructed to alleviate the numerical difficulties associated with the standard finite element methods. The examples include large deformation and fragment impact problems, modeling of microstructure evolution, and solution of Schrodinger equation in quantum mechanics.
  Alternatively, radial basis collocation method offers exponential convergence. However, the method is suffered from the large condition numbers due to its "nonlocal" approximation, and the nonlocality of radial basis function limits its application to small scale problems. In the second part of this talk, we show how to combine the advantages of radial basis function and reproducing kernel function to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence than that of Galerkin type reproducing kernel method.

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