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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/112026

    Title: Application of the Clifford algebra valued boundary integral equations with Cauchy-type kernels to some engineering problems
    Authors: 李家瑋
    Lee, Jia-Wei
    Contributors: 淡江大學土木系
    洪宏基;Hong, Hong-Ki;陳正宗;Chen, Jeng-Tzong
    Keywords: complex variable boundary integral equation;Clifford algebra;Clifford algebra valued boundary integral equation;Cauchy-type kernels
    Date: 2016-01
    Issue Date: 2017-11-09 11:08:47 (UTC+8)
    Abstract: The conventional complex variable boundary integral equation (CVBIE) based
    on the conventional Cauchy integral formula is powerful and suitable to solve
    two-dimensional problems. In particular, the unknown function is a complex-valued
    holomorphic function. In other words, the unknown function satisfies the
    Cauchy-Riemann equations. However, the most part of practical engineering
    problems are three-dimensional problems and do not necessarily satisfies
    Cauchy-Riemann equations. Therefore, there are two targets in this dissertation. One
    is to extend the conventional CVBIE to solve two-dimensional problems for which
    the unknown function is not a complex-valued holomorphic function. The other is to
    extend to three-dimensions and derive an extended BIE still preserving some
    properties of complex variables in the three-dimensional state. For the extension of
    the conventional CVBIE, we employ the Borel-Pompeiu formula to derive the
    generalized CVBIE. In this way, the torsion problems can be solved in the state of
    two shear stress fields directly. In addition, the torsional rigidity can also be
    determined simultaneously. Since the theory of complex variables has a limitation
    that is only suitable for 2-dimensional problems, we introduce Clifford algebra and
    Clifford analysis to replace complex variables to deal with 3-dimensional problems.
    Clifford algebra can be seen as an extension of complex or quaternionic algebras.
    Clifford analysis is also known as hypercomplex analysis. We apply the Clifford
    algebra valued Stokes' theorem to derive Clifford algebra valued BIEs with
    Cauchy-type kernels. In this way, some three-dimensional problem with multiple
    unknown fields may be solved straightforward. Finally, several electromagnetic
    scattering problems are considered to check the validity of the derived Clifford
    algebra valued BIEs.

    分方程。對於延伸傳統複變數邊界積分方程,本文使用 Borel-Pompeiu 公式來
    Appears in Collections:[Graduate Institute & Department of Civil Engineering] Thesis

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