Adaptive error estimation technique of the Trefftz method for solving the over-specified boundary value problem

K. H. Chen, C. T. Chen, J. F. Lee

研究成果: Article同行評審

5 引文 斯高帕斯(Scopus)

摘要

In this paper, numerical solutions are investigated based on the Trefftz method for an over-specified boundary value problem contaminated with artificial noise. The main difficulty of the inverse problem is that divergent results occur when the boundary condition on over-specified boundary is contaminated by artificial random errors. The mechanism of the unreasonable result stems from its ill-posed influence matrix. The accompanied ill-posed problem is remedied by using the Tikhonov regularization technique and the linear regularization method, respectively. This remedy will regularize the influence matrix. The optimal parameter λ of the Tikhonov technique and the linear regularization method can be determined by adopting the adaptive error estimation technique. From this study, convergent numerical solutions of the Trefftz method adopting the optimal parameter can be obtained. To show the accuracy of the numerical solutions, we take the examples as numerical examination. The numerical examination verifies the validity of the adaptive error estimation technique. The comparison of the Tikhonov regularization technique and the linear regularization method was also discussed in the examples.

原文English
頁(從 - 到)966-982
頁數17
期刊Engineering Analysis with Boundary Elements
33
發行號7
DOIs
出版狀態Published - 2009 七月 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

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