Boundary Integral Equations for Isotropic Linear Elasticity

High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The meth...

Integral Equations Formulation of Classical Elasticity

Artificial conditions for the linear elasticity equations

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the wellposedness except for a countable set of parameters. A perturbation...

Fast Algorithms for Boundary Integral Equations

This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order the fast multipole method and its kernel independent variant, the hierarchical matrix framework, the wavelet based method, the high frequency fast multipole method, and the recently proposed multi...

Sparse grids for boundary integral equations

The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on a square in IR 3. Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces are obtained.