TY - JOUR
T1 - Adaptive error estimation technique of the Trefftz method for solving the over-specified boundary value problem
AU - Chen, K. H.
AU - Chen, C. T.
AU - Lee, J. F.
N1 - Funding Information:
The authors are grateful to Prof. H. Power at 29th World Conference on BEM/MRM at Wessex Institute of Technology in Southampton, UK, for helpful comments. Financial support from the National Science Council under Grant no. NSC-95-2221-E-197-026-MY3 is gratefully acknowledged.
PY - 2009/7
Y1 - 2009/7
N2 - 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.
AB - 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.
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U2 - 10.1016/j.enganabound.2009.02.001
DO - 10.1016/j.enganabound.2009.02.001
M3 - Article
AN - SCOPUS:64049117725
SN - 0955-7997
VL - 33
SP - 966
EP - 982
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
IS - 7
ER -