Some integral identities for the fttndamental solutions of potential and elastostatic problems are established in this paper. With these identities it is shown that the conventional boundary integral equation (BIE), which is generally expressed in terms of singularintegrals in the sense of the Cauchy principal value (CPV), and the derivative BIE, which is similarly expressed in terms of hypersi...

Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior domains. The practical application of these methods, however, requires the accurate evaluation of boundary integrals with singular, weakly singular or nearly sing...

with the effects of electric charges at rest. For modern electron and microelectromechanical systems (MEMS), an accurate electrostatic analysis is both essential and indispensable. We know that if we use the conventional boundary element method (BEM) for electrostatic problems that have singularity due to degenerate boundaries, the coincidence of the boundaries gives rise to a difficult, or ill...

A symmetric Galerkin boundary-element method is used for the solution of boundary-value problems with mixed boundary conditions of Dirichlet and Neumann type. As a model problem we consider the Laplace equation. When an iterative scheme is employed for solving the resulting linear system, the discrete boundary integral operators are realized by the fast multipole method. While the single-layer ...

Among the well-known constants in the theory of boundary integral equations are the coercivity constants of the single layer potential and the hypersingular boundary integral operator, and the contraction constant of the double layer potential. Whereas there have been rigorous studies how these constants depend on the size and aspect ratio of the underlying domain, only little is known on their...

To study the interaction of a vibrating shallow shell with three-dimensional subsonic gas flow, we deduce system hypersingular integral equations for aerodynamic derivatives pressure drop. This is convenient solution problems aeroelasticity. We solve by using numerical approach based on discrete vortex method. model vibrations shells, ordinary differential help assumed-mode also perform investi...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

A nonsingular integral formulation for the Helmholtz eigenproblem is developed in this paper. This novel method contains only imaginary-part kernels instead of complex-part kernels in the complexvalued BEM. Based on the imaginary-part formulation without singular source, no singular or hypersingular integrals are present. Although this formulation avoids the computation of singular and hypersin...