- Cubature guidelines primarily based on bivariate spline quasi-interpolation for weakly singular integrals(arXiv)
Creator : A. Falini, T. Kanduč, M. L. Sampoli, A. Sestini
Summary : On this paper we current a brand new class of cubature guidelines with the purpose of precisely integrating weakly singular double integrals. Specifically we give attention to these integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary worth issues, utilizing a collocation methodology throughout the Isogeometric Evaluation paradigm. In such setting the common a part of the integrand might be outlined because the product of a tensor product B-spline and a common operate. The principles are derived by utilizing first the spline quasi-interpolation strategy to approximate such operate after which the extension of a well-known algorithm for spline product to the bivariate setting. On this means effectivity is ensured, because the locality of any spline quasi-interpolation scheme is mixed with the aptitude of an advert — hoc remedy of the B-spline issue. The numerical integration is carried out on the entire help of the B-spline issue by exploiting inter-element continuity of the integrands
