Integral equation analysis of the driven-cavity boundary singularity

The Boundary Integral Equation Method

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 ...

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

Boundary integral equation for inclusion and cavity shape sensitivity in harmonic elastodynamics

In many inverse and optimization problems, the computation of the gradient of the response—displacements and tractions—at the boundary of specimens due to a variation of the geometry is needed. Since finite difference techniques are error prone due to the difference parameter and are computationally expensive, a formulation to compute this gradient by direct differentiation is developed based o...

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...