Boundary Integral Equations in Clifford Analysis
Date Issued
2008
Date
2008
Author(s)
Lin, Kuan-Fu
Abstract
It is well known that plane problems of harmonic functions are analyzed and solved effectively when expressed in the form of complex variables. This effectiveness is generally attributed to the powerful techniques of complex analysis and the richness of complex function theory. In view of this, the present thesis is aimed to extend the techniques to n-dimensional problems of boundary integral equations (BIEs) for harmonic field variables. Regarding usefulness for practical purposes, we derive singular and hypersingular BIEs not only for points on smooth boundaries but also for corner boundary points. The relations of real, complex, quaternion, and Clifford valued BIEs are explored. In Clifford valued BIEs, the three types of functions of are treated.
Subjects
singular boundary integral equation
hypersingular boundary integral equation
Laplace equation
Dirac equation
complex analysis
Clifford analysis
Type
thesis
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