THE BOUNDARY FACE METHOD WITH VARIABLE APPROXIMATION BY B-SPLINE BASIS FUNCTION

Abstract

B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.