Zeitschrift für Angewandte und Computermathematik

Realization of Convergence Splines/ NURBS of Higher Order Stability in Isgeometric Analysis

Abstract

Mohd Taib Shatnawi

Conventional B-splines lack the capacity of local refinement that is required in order to realize ideal convergence order in genuine applications. The challenges with the isogeometric approach include the need to develop an alternative mathematical approach of higher-order equations proven to converge to the shape interface. The main purpose of this study is to determine the realization approach for isogeometric structure in convergence splines/NURBS of distinctive nature of higher-order stability. The basis for this realization approach (i.e. convergence splines/NURBS of higherorder) for B-Spline is degree (order) of realization as used in B-Spline theory. In this approach, the converging (C) order of the basis functions is elevated. An ideal (new) isogeometric structure (i.e. curve or mesh) in convergence splines/NURBS of higher-order stability for improved local refinement has been realized. It is clear that when the order C is enhanced (i.e. realized), converging number n must also be enhanced (i.e. realized) by the equivalent amount of degree. In the process of order enhancement (i.e. the order realization), the stability of every knot value is elevated. Order realization initiates by replicating present knots by the equivalent number as the increase in converging order. In this, every knot vector value is elevated by one point. In line with this, the amount of control points and the basic functions are boosted or amplified from 8 to 13. The refined control points computed was improved where the convergence of higher-order was realized.