Wave Elevation for an Array of Columns Under Wave-Current Interactions

A wave and current diffraction model is developed based on the potential flow theory and a high-order boundary element method with the successful treatment of singular and nearly singular integrals. The wave-current diffraction from four mounted cylindrical columns are computed, and the free surface wave elevations among the columns are investigated. The influences of the current speed, wave direction, and column spacing on the wave elevation are examined. Ultimately, the presence of a current has a significant influence on the magnitude, spatial location and occurrence frequency of the maximum wave elevation.

Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

Error Estimates for the Nearly Singular Momentum-Space Bound-State Equations

We present errors of quadrature rules for the nearly singular integrals in the momentum-space bound-state equations and give the critical value of the nearly singular parameter. We give error estimates for the expansion method, the Nyström method, and the spectral method which arise from the near singularities in the momentum-space bound-state equations. We show the relations amongst the near singularities, the odd phenomena in the eigenfunctions, and the unreliability of the numerical solutions.

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

Interlaminar Stresses Analysis of Three-Dimensional Composite Laminates by the Boundary Element Method

In engineering industries, composite laminates have been widely applied for various applications. This work presents an efficient analysis of the interlaminar stresses in three-dimensional thin layered anisotropic composites by the boundary element method (BEM). Due to the nearly singular integrals in the boundary integral equation, the conventional BEM approach cannot be applied to analyze the composite layers that are very thin. The present work employs the self-regularization scheme to analyze the interlaminar stresses in thin anisotropic composites. In the end, a few benchmark examples are presented to show the applicability of the present approach.