Finite element application of ERBS extraction

[摘要] In this paper we explore ERBS extraction in application to a heat conduction problem. Two types of basis functions are considered: B-spline and expo-rational B-spline (ERBS) combined with Bernstein polynomials. The first one is a global basis defined on a subdomain whose size is related to the spline degree, while the second one is a strictly local basis under the local geometry. While all the coefficients of the B-spline tensor product surface affect each element of the patch, local surfaces of the blending surface conserve both local manipulation and smoothness of the global surface. We show the conversion between these bases by using an ERBS extraction. The extraction operator allows us to convert the control points of the surface evaluated by B-splines to control points of the ERBS surface and vice versa. This approach is demonstrated on an example of the finite element solution approximation of the heat equation. (C) 2020 The Author(s). Published by Elsevier B.V.

[发布日期] 2020-12-01

[关键词] Isogeometric analysis;Local projection;Extraction operator;Expo-rational basis functions