Finite element application of ERBS extraction

Abstract

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 strictlylocal 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.<p>

<p>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.