NLFEM with higher order interpolation function for efficient analysis of irregular domain.

Abstract

This study proposes a new approach to developing a more efficient numerical technique by coupling the non-uniform rational B-spline (NURBS) with the higher-order polynomial basis functions under the framework of the Finite Element Method (FEM). In this technique, denoted as NURBS-Lagrange FEM (NLFEM), the NURBS basis functions are employed to represent the geometry of the problem domain, while the Lagrange interpolation functions are employed for the higher-order polynomial functions to interpolate the field variables. The NURBS is a mathematical model which provides a numerically stable algorithm to exactly represent all conic sections, and the Lagrange interpolation function allows for higher-order basis functions resulting in a faster convergence rate of analysis. By taking advantage of both models, the objective of this study is to propose a new approach, i.e., NLFEM, which can improve the accuracy of the analysis of the irregular domain with more efficient consumption of computer resources. A steady heat transfer formulation for a curved boundary problem is presented to demonstrate the validity and accuracy of the developed technique. The performance is verified against converged solutions obtained using higher-order FEM (FEM/Q9) and NURBS-Augmented FEM (NAFEM). The presented result shows that the NLFEM provides a favorable comparison against other methods. The converged solution is achieved 20% faster than the FEM/Q9 and 80 % faster than the NAFEM. This highlights the potential of the NLFEM as a new approach in numerical techniques for solving problems with irregular boundaries.