In this paper, we establish that the Lagrangian-type material differentiation formulas, that allow to express the first-order derivative of a (regular) surface integral with respect to a geometrical domain perturbation, still hold true for the strongly singular and hypersingular syrface integrals usually encountered in boundary integral formulations. As a consequence, this work supports previou...

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to onedimensional Fredholm integral equations of the second kind. If th...

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, sin...

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. For hypersingular integral equations in 2D with positive-order Sobolev space, we analyze the mathematical relation between the h − h/2error estimator from [18], the two-level error estimator from [22], and the averaging error estimator from [7]. All of these a posteriori error e...

In this paper we analyze the numerical solution by a collocation method of a hypersingular integral equation resulting from the boundary value problem related to an infinite strip containing an edge crack perpendicular to its boundaries. Moreover, we show convergence results as well as numerical tests in a case of interest in fracture mechanics.

The problem of three-dimensional potential flow past a thin rigid screen is reduced to a hypersingular boundary integral equation. This equation is then projected onto a flat reference screen, which is taken to be a circular disc. Solutions are obtained for screens that are axisymmetric perturbations from the disc, so that the screen is rippled concentrically. The added mass is calculated for a...

Four integral identities for the fundamental solution of thin plate bending problems are presented in this paper. These identities can be derived by imposing rigid-body translation and rotation solutions to the two direct boundary integral equations (BIEs) for plate bending problems, or by integrating directly the governing equation for the fundamental solution. These integral identities can be...

where 0 < ε < 1, and the unknown function g satisfies the boundary conditions g(±1) = 0. The integral has to be understood as the finite part of the strongly singular integral in the sense of Hadamard, who introduced this concept in relation to the Cauchy principal value. In fact, the toughness of brittle solids such as ceramics and cement-like materials can be increased considerably by the use...