A collocation method for a hypersingular boundary integral equation via trigonometric differentiation
نویسندگان
چکیده
منابع مشابه
On the collocation method for a nonlinear boundary integral equation
In this paper we study a potential problem with a nonlinear boundary condition. Using the Green representation formula for a harmonic function we reformulate the nonlinear boundary value problem as a nonlinear boundary integral equation. We shall give a brief discussion of the solvability of the integral equation. The aim of this paper, however, is to analyse the collocation method for finding ...
متن کاملThe numerical solution of a nonlinear hypersingular boundary integral equation
In this paper we consider a direct hypersingular integral approach to solve harmonic problems with nonlinear boundary conditions by using a practical variant of the Galerkin boundary element method. The proposed approach provides an almost optimal balance between the order of convergence and the numerical effort of work to compute the approximate solution. Numerical examples confirm the theoret...
متن کاملExplicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method
This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and...
متن کاملA Discrete Collocation Method for Boundary Integral Equations
We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...
متن کاملA fast algorithm for solving nonlinear hypersingular integral equation
where 0 < ε < 1, and the unknown function g satisfies the boundary conditions g(±1) = 0. The integral has to be understood as the finite part of the strongly singular integral in the sense of Hadamard, who introduced this concept in relation to the Cauchy principal value. In fact, the toughness of brittle solids such as ceramics and cement-like materials can be increased considerably by the use...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Integral Equations and Applications
سال: 2014
ISSN: 0897-3962
DOI: 10.1216/jie-2014-26-2-197