... to a set of integral equations having square-root singularities at the submerged edges of thin structures. To address such singularities, a multi-term Galerkin approximation technique is used along with Chebyshev polynomials (multiplied with suitable weights) as basis functions. The numerical methodology...

... in the frequency domain. After removing the singularities in the boundary integral equation and representing the body surface exactly by either analytical description or NURBS surfaces, the boundary integral equation can be discretized over the exact body surface by Gaussian quadratures. Accuracy of the method...

..., an implicit matching can be done. When a volume-discretization method is used in the interior region, a newly developed explicit matching procedure is performed. Demonstrations of the transparent properties of this shell are made for several types of unsteady problems. integral equations time-domain...

... are considered. It may be surface-piercing or bottom-standing, or in the form of a submerged block not extending down to the bottom, or in the form of a thick wall with a submerged gap. Multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving first-kind integral equations...