A Conjugate Boundary Element Method for Complex Analysis of Analytic Function

LI Guo-qing

doi:10.21656/1000-0887.370315

Volume 38 Issue 8

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LI Guo-qing. A Conjugate Boundary Element Method for Complex Analysis of Analytic Function[J]. Applied Mathematics and Mechanics, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315

Citation:

LI Guo-qing. A Conjugate Boundary Element Method for Complex Analysis of Analytic Function[J]. Applied Mathematics and Mechanics, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315

Citation:

LI Guo-qing. A Conjugate Boundary Element Method for Complex Analysis of Analytic Function[J]. Applied Mathematics and Mechanics, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315

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A Conjugate Boundary Element Method for Complex Analysis of Analytic Function

doi: 10.21656/1000-0887.370315

LI Guo-qing

Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P.R.China

Funds: The National Natural Science Foundation of China(10972083)

Received Date: 2016-10-17
Rev Recd Date: 2016-12-08
Publish Date: 2017-08-15

Abstract

Abstract

An analytic function is composed of 2 real conjugate harmonic functions, of which the complex analysis plays an important role in the fields of applied mathematics and mechanics. A set of weighted residual equations were proposed and proved to be equivalent to the approximate solution to the original problem involving 2 governing equations in the domain, the boundary condition and the CauchyRiemann equation at the boundary. 2 conventional direct boundary integral equations at the boundary collocation points were deduced from 2 of the weighted residual equations, and 1 finite difference equation was deduced from the rest one. The mathematical problem arising from the illconditioned linear equations was solved and the Cauchy integral equation was adopted for numerical calculation of the fields at the internal points inside the domain. Finally, the proposed conjugate boundary element method with constant elements was completely established. 3 examples demonstrate that, the proposed method is valid for analytic functions in terms of the power function, the exponential function and the logarithmic function in interior or exterior domains, and the error estimation of the proposed method is at the same order as that of the boundary element method for 2D potential problems.
- complex analysis,
- boundary element,
- analytic function,
- potential theory

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References(18)

References

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