We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar soundsoft (Dirichlet) and sound-hard (Neumann) screens. We prove continuity and coercivity of the relevant boundary integral operators (the acoustic single-layer and hypersingular operators respectively) in appropriate fractional Sobolev spaces, with wavenumber-explicit bou...

Consider a three-dimensional homogeneous isotropic elastic solid containing a flat pressurized crack, fi. The problem of finding the resulting stress distribution can be reduced to a hypersingular integral equation over Q for the crack-opening displacement. Here, this equation is transformed into a similar equation over a circular region D, using a conformal mapping between Q and D. This new eq...

This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and...

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly si...

The solution to the elastodynamic equation in exterior of a polyhedral domain or screen exhibits singular behavior from corners and edges. detailed expansion singularities implies quasi-optimal estimates for piecewise polynomial approximations Dirichlet trace traction. results are applied hp graded versions time boundary element method weakly hypersingular integral equations. Numerical examples...

This paper is concerned with the boundary integral equation method for solving exterior Neumann value problem of dynamic poroelasticity in two dimensions. The main contribution this work consists aspescts: proposal a novel regularized equation, and presentation new formulations strongly singular hyper-singular operators. First, turning to spectral properties double-layer operator corresponding ...