Adaptive Hierarchical Isogeometric Finite Element Methods

1. Front Matter

   Pages I-XIX

   PDF

2. Introduction

   • Anh-Vu Vuong

   Pages 1-5

3. Prerequisites from Applied Geometry and Spline Theory

   • Anh-Vu Vuong

   Pages 7-18

4. Mathematical Modelling and Finite Element Analysis

   • Anh-Vu Vuong

   Pages 19-45

5. Isogeometric Analysis

   • Anh-Vu Vuong

   Pages 47-78

6. Local Refinement for Isogeometric Analysis

   • Anh-Vu Vuong

   Pages 79-114

7. Conclusions

   • Anh-Vu Vuong

   Pages 115-115

8. Back Matter

   Pages 117-127

   PDF

​Isogeometric finite elements combine the numerical solution of partial differential equations and the description of the computational domain given by rational splines from computer aided geometric design. This work gives a well-founded introduction to this topic and then extends isogeometric finite elements by a local refinement technique, which is essential for an efficient adaptive simulation. Thereby a hierarchical approach is adapted to the numerical requirements and the relevant theoretical properties of the basis are ensured. The computational results suggest the increased efficiency and the potential of this local refinement method.

• Isogeometric Analysis
• Local Refinement for Isogeometric Analysis
• Mathematical Models and Finite Element Analysis
• Prerequisites form Applied Geometry and Spline Theory

• Kaiserslautern, Germany

  Anh-Vu Vuong

Anh-Vu Vuong received his doctor’s degree under supervision of Prof. Dr. Bernd Simeon at the Centre for Mathematical Sciences of the TU Munich in the context of the research project EXCITING funded by the European Union. He now works at the Felix-Klein-Centre for Mathematics of the University of Kaiserslautern.

Policies and ethics