After successful completion of the course, students are able to explain and utilize the basic approaches regarding modeling in CAD systems and in the classic finite element simulation. They will be able to combine these two approaches to isogeometric analysis and can handle its application to various classes of problems (structural mechanics, heat transfer and CFD) under consideration of the pros and cons. A focus area of the course will be the particularities of isogeometric analysis as compared to standard finite elements, in particular in terms of quadrature and assembly.

The students will have written their own isogeometric analysis program in Matlab and will have detailed knowledge of the components relevant to such a program. 

• Geometry representation (Bézier splines, B-splines, NURBS, T-splines)
• Geometry manipulation and derivatives
• Isogeometric analysis in comparison to standard finite elements
• Assembly 
• Quadrature
• Refinement
• Imposition of boundary conditions
• Trimmed NURBS in isogeometric analysis
• Applications of IGA

The lecture makes use of different multi-media elements, combining slides with hand-written parts. Furthermore, the lecture contains interactive concepts such as quizzes or online programs. Finally, the exercise in Matlab teaches the students hands-on, what isogeometric analysis demands of the user. 

Due to the Covid 19 pandemic, the mode of the class may differ

Performance is assessed by means of an oral examination. The oral examination consists of two parts. 12 points can be achieved in each part. Part 1 of the oral examination is a short presentation, in part 2 general questions on the entire lecture material are asked. The topic of the short presentation can be chosen by the students from a list of suggested presentations that will be announced in TUWEL. Handwritten notes may be prepared for the short presentation. The following criteria apply to the assessment of the short presentation:

Content

Gross errors in the content or failure to address the topic. 0 points
Content correct in essential points and corresponding to the topic in all relevant points. 3 points
Content almost completely correct and fully in line with the topic 6 points

Originality

The presentation corresponds almost completely to that of the lecture. 0 points
The presentation is based on the lecture, but was arranged independently. 2 points
Presented content goes beyond the lecture by drawing own conclusions. 4 points

Presentation

The handwritten notes are difficult to read and the oral presentation was not comprehensible. 0 points
The handwritten notes had slight weaknesses in the preparation and the oral presentation was mostly comprehensible. 1 point
The handwritten notes were well prepared and the oral presentation was clearly comprehensible. 2 points

Basic knowledge of the finite element method