Polytope Mesh Generation and Finite Element Analysis Methods

The project is part of a research group focusing on creating new tools for simulating problems in solid mechanics. In particular, we aim to develop a type of mathematical element called "weakly star shaped spline elements" (WS3E), and use a method called the scaled boundary isogeometric analysis (SBIGA) for numerical simulation. Our three main goals are (1) to divide the object we are studying, which is called the "domain", into WS3Es, (2) learn how to generate them accurately, and (3) find ways to make the overall process faster and more efficient. This project will help the research group by providing the technology needed to create numerical simulations using scaled boundary isogeometric analysis. The goal is to find a way to represent domains representing two-dimensional and three-dimensional objects that are easy to create and exchange data with Computer Aided Design systems, while also being useful for design optimization. This will help integrate design and analysis seamlessly and create digital models of objects and environments. To achieve this, the research unit will combine the work of experts in geometry and simulation to develop new ways of representing domains and simulating physical phenomena by solving partial differential equations. We will work with our partners in the research group to see how we can use the WS3Es from our project in a classical method for numerical simulation, which is called the "scaled boundary finite element method" and serves as the starting points for the new developments. We will also study spline level set surfaces. Additionally, we will investigate the structure of parameterizations and how singularities affect them. We will also continue our earlier work on spline refinement. Finally, we plan to collaborate on the use of machine learning to help us create interfaces and solve parameterization problems.