- Cubature pointers based totally on bivariate spline quasi-interpolation for weakly singular integrals(arXiv)
Creator : A. Falini, T. Kanduč, M. L. Sampoli, A. Sestini
Abstract : On this paper we present a model new class of cubature pointers with the aim of exactly integrating weakly singular double integrals. Particularly we give consideration to those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary price points, using a collocation methodology all through the Isogeometric Analysis paradigm. In such setting the frequent part of the integrand is likely to be outlined as a result of the product of a tensor product B-spline and a typical function. The ideas are derived by using first the spline quasi-interpolation technique to approximate such function after which the extension of a well known algorithm for spline product to the bivariate setting. On this implies effectivity is ensured, as a result of the locality of any spline quasi-interpolation scheme is blended with the aptitude of an advert — hoc treatment of the B-spline difficulty. The numerical integration is carried out on the whole assist of the B-spline difficulty by exploiting inter-element continuity of the integrands
