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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50480

Title: On Solving the Direct/Inverse Cauchy Problems of Laplace Equation in a Multiply Connected Domain, Using the Generalized Multiple-Source-Point Boundary-Collocation Trefftz Method & Characteristic Lengths
Authors: Weichung Yeih
Chein-Shan Liu
Chung-Lun Kuo
Satya N. Atluri
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: modified collocation Trefftz method
Laplace equation
direct problem
inverse problem
addition theorem
generalized multiple-source collocation Trefftz method
Date: 2010-03
Issue Date: 2018-10-12T03:04:00Z
Publisher: CMC: Computers, Materials, & Continua
Abstract: Abstract: In this paper, a multiple-source-point boundary-collocation Trefftz
method, with characteristic lengths being introduced in the basis functions, is proposed
to solve the direct, as well as inverse Cauchy problems of the Laplace equation
for a multiply connected domain. When a multiply connected domain with
genus p (p>1) is considered, the conventional Trefftz method (T-Trefftz method)
will fail since it allows only one source point, but the representation of solution
using only one source point is impossible. We propose to relax this constraint by
allowing many source points in the formulation. To set up a complete set of basis
functions, we use the addition theorem of Bird and Steele (1992), to discuss how
to correctly set up linearly-independent basis functions for each source point. In
addition, we clearly explain the reason why using only one source point will fail,
from a theoretical point of view, along with a numerical example. Several direct
problems and inverse Cauchy problems are solved to check the validity of the proposed
method. It is found that the present method can deal with both direct and
inverse problems successfully. For inverse problems, the present method does not
need to use any regularization technique, or the truncated singular value decomposition
at all, since the use of a characteristic length can significantly reduce the
ill-posed behavior. Here, the proposed method can be viewed as a general Trefftz
method, since the conventional Trefftz method (T-Trefftz method) and the method
of fundamental solutions (F-Trefftz method) can be considered as special cases of
the presently proposed method.
Relation: 17(3) pp.275-302
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50480
Appears in Collections:[河海工程學系] 期刊論文

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