Extrapolation Algorithms for Solving Mixed Boundary Integral Equations of the Helmholtz Equation by Mechanical Quadrature Methods

2010 ◽  
Vol 31 (6) ◽  
pp. 4115-4129 ◽  
Author(s):  
Jin Huang ◽  
Zhu Wang
Keyword(s):  
Helmholtz Equation ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
Mechanical Quadrature ◽  
Quadrature Methods

Mechanical Quadrature Methods and their Extrapolations for Axisymmetric Flow past the Torus of Anchor Ring

2012 ◽  
Vol 614-615 ◽  
pp. 617-620
Author(s):  
Xin Luo ◽  
Jin Huang
Keyword(s):  
Convergence Rate ◽  
Integral Equations ◽  
Potential Theory ◽  
Flow Problem ◽  
Boundary Integral Equations ◽  
Axisymmetric Flow ◽  
Boundary Integral ◽  
Extrapolation Methods ◽  
Mechanical Quadrature ◽  
Quadrature Methods

By the potential theory, axisymmetric flow problem is converted into boundary integral equations (BIEs). The mechanical quadrature methods (MQMs) are presented to deal with the singularities in the integral kernels, which are simple without any singularity integral computation. In addition, the convergence rate of the MQMs can be improved by using the extrapolation methods (EMs). The efficiency of the algorithms is illustrated by examples.

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