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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(More)
By potential theorem, the fundamental boundary eigenproblem problems are converted into bound-ary integral equations(BIE) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQM) are presented to obtain the eigensolutions (λ_1 λ, u˜_1) and the eigensolutions are used to solve the potential problems, which(More)
By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the(More)
Elastic boundary value problems of the third kind are converted into boundary integral equations (BIE) with the logarithmic singularity and the Hilbert singularity. In this paper, quadrature methods are presented to deal with the logarithmic singularity and the Hilbert singularity simultaneously for solving the BIE, which possesses the high accuracies(More)
We study the numerical solution procedure for two-dimensional Laplace’s equation subjecting to non-linear boundary conditions. Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature methods are presented for solving the equations, which possess high accuracy order O(h 3) and low(More)
For solving linear systems , different preconditioned methods have been proposed by many authors. In this paper, a preconditioned iterative method is presented with a new preconditioner, based on the type preconditioning matrices provided by Hadjidjmos et al. [1] and Evans et al. [2]. The corresponding convergence and comparison results are given and some(More)
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