The short note concerns with elasticity problems involving singular and hypersingular integrals over open surfaces, specifically cracks, with the contour propagating in time. Noting that near a smooth part of a propagating contour the state is asymptotically plane, we focus on 1D hypersingular integrals and employ complex variables. By using the theory of complex variable singular and hypersing...

In the numerical treatment of integral equations of the first kind using boundary element methods (BEM), the author and E. P. Stephan have derived a posteriori error estimates as tools for both reliable computation and self-adaptive mesh refinement. So far, efficiency of those a posteriori error estimates has been indicated by numerical examples in model situations only. This work affirms effic...

Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moment’s discretization to the hypersingular volume integral equation in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green’s function and the contrast source over the domain of interest. For electrically l...

A low-frequency fast multipole boundary element method (FMBEM) for 3D acoustic problems is proposed in this paper. The FMBEM adopts the explicit integration of the hypersingular integral in the dual boundary integral equation (BIE) formulation which was developed recently by Matsumoto, Zheng et al. for boundary discretization with constant element. This explicit integration formulation is analy...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one t...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to ch...

While an integration by parts formula for the bilinear form of hypersingular boundary integral operator transient heat equation in three spatial dimensions is available literature, a proof this seems to be missing. Moreover, contains term including time derivative fundamental solution equation, whose interpretation difficult at second glance. To fill these gaps, we provide rigorous general vers...

The present paper deals with a boundary element formulation based on the traction elasticity boundary integral equation (potential derivative for Laplace’s problem). The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the ...

In this paper we describe a high order spectral algorithm for solving the time-harmonic Navier equations in the exterior of a bounded obstacle in three space dimensions, with Dirichlet or Neumann boundary conditions. Our approach is based on combined-field boundary integral equation (CFIE) reformulations of the Navier equations. We extend the spectral method developped by Ganesh and Hawkins [12...