scholarly journals Symmetric Complex Boundary Element Scheme for 2-D Stokes Mixed Boundary Value Problem

2016 ◽  
Vol 13 (1) ◽  
Author(s):  
Sun-Gwon Hong
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Element Scheme ◽  
Boundary Limit ◽  
Complex Boundary ◽  
Gt Element

For 2-D Stokes mixed boundary value problems we construct a boundary<br />integral equation which couples a conventional boundary integral equation<br />for the velocity with a hypersingular boundary integral equation for the<br />traction. Expressing terms in the equation by complex variables, we obtain a<br />complex boundary integral equation and realize symmetrization of boundary<br />element scheme by Galerkin method. Applying a boundary limit method, we<br />obtain exact calculation formulae for calculation of hypersingular boundary<br />integrals. It is shown that all divergent terms in hypersingular integrals<br />cancel each other out.

scholarly journals Regularization of the Divergent Integrals. I. General Consideration.

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
Vladimir Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
General Consideration ◽  
Science And Engineering ◽  
Hypersingular Integrals ◽  
Weakly Singular ◽  
Easy Calculation ◽  
Multidimensional Integrals

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals, have been constructed. Such approach may be easily generalized and applied to the calculation of multidimensional integrals with singularities of various types.

scholarly journals A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohamed M. S. Nasser ◽  
Ali H. M. Murid ◽  
Samer A. A. Al-Hatemi
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
Numerical Examples ◽  
Multiply Connected ◽  
Generalized Neumann Kernel ◽  
Multiply Connected Regions ◽  
Neumann Kernel

We present a uniquely solvable boundary integral equation with the generalized Neumann kernel for solving two-dimensional Laplace’s equation on multiply connected regions with mixed boundary condition. Two numerical examples are presented to verify the accuracy of the proposed method.

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