Complex variable boundary integral equations for perforated infinite planes

Complex variable boundary integral equations for perforated in nite planes

Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

Fast Algorithms for Boundary Integral Equations

This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order the fast multipole method and its kernel independent variant, the hierarchical matrix framework, the wavelet based method, the high frequency fast multipole method, and the recently proposed multi...

Sparse grids for boundary integral equations

The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on a square in IR 3. Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces are obtained.

Piecewise Polynomial Collocation for Boundary Integral Equations

This paper considers the numerical solution of boundary integral equations of the second kind for Laplace s equation u on connected regions D in R with boundary S The boundary S is allowed to be smooth or piecewise smooth and we let f K j K Ng be a triangulation of S The numerical method is collocation with approximations which are piecewise quadratic in the parametrization variables leading to...