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 methods possess high accuracy O(h) and low computing complexity. The convergence and stability are proved based on Anselone’s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples. Keywords—boundary integral equation, extrapolation algorithm, a posteriori error estimate, elasticity.