Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method

A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems

A low-frequency fast multipole boundary element method (FMBEM) for 3D acoustic problems is proposed in this paper. The FMBEM adopts the explicit integration of the hypersingular integral in the dual boundary integral equation (BIE) formulation which was developed recently by Matsumoto, Zheng et al. for boundary discretization with constant element. This explicit integration formulation is analy...

The 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...

Dispersion analysis of the meshless local boundary integral equation (LBIE) method for the Helmholtz equation

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...

A Semi-Analytical Method for the Solution of Helmholtz Equation

This note is concerned with a semi-analytical method for the solution of 2-D Helmholtz equation in unit square. The method uses orthogonal functions to project the problem down to finite dimensional space. After the projection, the problem simplifies to that of obtaining solutions for second order constant coefficient differential equations which can be done analytically. Numerical results indi...

The Boundary Integral Equation Method