An empirical error analysis of the boundary element method applied to Laplace's equation

BOUNDARY ELEMENT METHOD APPLIED TO THE LIFTING BODIES NEAR THE FREE SURFACE

In this study, the boundary element method is formulated to evaluate hydrodynamic characteristics of bodies including free surface effect. The method is based on two equations, the perturbation potential boundary integral and the pressure Kutta condition, which are solved simultaneously. The method uses isoparametric elements for both quantity and geometric on the boundary. The method is first ...

Richardson extrapolation applied to boundary element method results in a Dirichlet problem for the Laplace equation

Fast Multipole Boundary Element Method for 2-D Helmholtz Equation Problems and Its Error Analysis ?

In this paper, a kind of Fast Multipole Boundary Element Method (FM-BEM) based on series form expansion is presented to solve two-dimensional (2-D) Helmholtz equation problems. A theorem of multipole expansion is derived and proved for the fundamental solution, which demonstrates the error source and can be widely used in 2-D electromagnetics and acoustics problems. The truncation error is anal...

The Hybrid Boundary Element Method Applied to Linear Fracture Mechanics

The hybrid boundary element method, a variational formulation introduced in 1987 by the first author, has proven to be a powerful tool for dealing with a great variety of problems of potential, elastostatics and elastodynamics. One of the most recent endeavors of the research team at PUC-Rio is the application of the method to problems of the linear elastic fracture mechanics. In the M.Sc. diss...

Modified F-Expansion Method Applied to Coupled System of Equation

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...