Immersogeometric finite element methods

Dominik Schillinger

April 9, 2015, 3 p.m. S2 416-2

Standard finite element methods are based on meshes that conform to the geometric boundaries of the analysis domain. This approach satisfies established mathematical paradigms and has many advantages, e.g., for imposing boundary conditions. However, in particular for image based geometric models, it also entails labor-intensive procedures, such as image segmentation, geometry cleanup, and mesh generation. An alternative approach is to immerse the analysis domain into a non-boundary-fitted mesh, which eliminates the need for image segmentation and alleviates many meshing related obstacles.

In this talk, I will first give an introduction to immersogeometric finite element methods, drawing on earlier work on the finite cell method. Influenced by isogeometric analysis, where the importance of eliminating geometric errors has gained broader recognition, the key feature of an immersogeometric method is the ability to faithfully represent the geometry of the immersed domain. I will show that weak imposition of boundary conditions and geometry-aware quadrature rules in intersected elements are the two key ingredients for accurate results, giving examples from both structural and fluid analysis. Finally I will illustrate the advantages of immersogeometric analysis with several larger-scale applications, e.g., the fully automated aerodynamic analysis of a full-scale tractor or the large deformation fluid-structure analysis of a bioprosthetic heart valve design.