A fast spectral Galerkin method for hypersingular boundary integral equations in potential theory

2009 ◽  
Vol 44 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Sylvain Nintcheu Fata ◽  
Leonard J. Gray
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Potential Theory ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Spectral Galerkin Method

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.

scholarly journals On the solution of the Helmholtz equation on regions with corners

2016 ◽  
Vol 113 (33) ◽  
pp. 9171-9176 ◽  
Author(s):  
Kirill Serkh ◽  
Vladimir Rokhlin
Keyword(s):  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Potential Theory ◽  
Bessel Functions ◽  
Boundary Integral Equations ◽  
Numerical Algorithms ◽  
Boundary Integral ◽  
Numerical Examples ◽  
Polygonal Domains

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

A Direct Method for Boundary Integral Equations on a Contour with a Peak

2003 ◽  
Vol 10 (3) ◽  
pp. 573-593
Author(s):  
V. Maz'ya ◽  
A. Soloviev
Keyword(s):  
Integral Equations ◽  
Potential Theory ◽  
Boundary Integral Equations ◽  
Direct Method ◽  
Logarithmic Potential ◽  
Boundary Integral ◽  
Logarithmic Potential Theory ◽  
A Direct Method

Abstract Boundary integral equations in the logarithmic potential theory are studied by the direct method under the assumption that the contour has a peak.

Sign in / Sign up

Export Citation Format

Share Document