Development of complex-variable differentiation method and its application in isogeometric analysis

Abstract

The complex-variable differentiation method (CVDM) is a very promising method to compute derivatives of complicated functions and is free from cancellation errors which often occur in the finite difference method. In this paper, CVDM is developed for the two-variable situation and is first applied to the isogeometric analysis method in which the computation of derivatives of rational functions represented by non-uniform rational B-splines (NURBS) method is very complicated. An example about h-refinement is given and the computational results show that the derived formulations in the paper is correct and the computation of derivatives using CVDM in isogeometric analysis is much simpler than using the traditional NURBS derivative formula.

Keywords:

• Complex-variable differentiation method
• isogeometric analysis
• NURBS
• B-spline
• h-refinement
• point inversion

Additional information

Notes on contributors

J X Hu

In 2003, Jinxiu Hu was admitted to the Science College of Xidian University, China, and became a student majoring in mathematics and applied mathematics. After four years study, she was recommended as a graduate student to the graduate school of Xidian University for further study in the same major. In 2010, she was enrolled to Dalian University of Technology to pursuit her Doctorate in the area of fluid mechanics in directions of boundary element method, isogeometric analysis, and proper orthogonal decomposition focused on their applications in engineering problems and solving large-scale systems of equations.

X W Gao

Xiaowei Gao is a professor at Dalian University of Technology, China. He obtained his Doctorate in 1999 at University of Glasgow, UK, in computational mechanics. He has published more than 100 journal papers and one book titled Boundary Element Programming in Mechanics, Cambridge University Press, 2002 (ISBN: 052177359-8). His research interests include boundary area method, computational heat transfer, computational solid and fluid mechanics, and multiple field coupling problems.