HPC cut finite element methods for multi-physics problems
The proposed research project seeks to extend an emerging finite element framework for discretization of multi-domain/multi-physics problems on unfitted domains with parallel computing capabilities. Multi-domain and multi-physics problems with interfaces can be severely limited by the use of conforming meshes when complex or evolving geometries in three spatial dimensions are involved. For instance, fluid-structure interaction problems with large deformations or free surface fluid problems with topological changes might render even recent algorithms for moving meshes (arbitrary Lagrangian-Eulerian based algorithms) infeasible. Another related problem class is the design of optimal shapes in industrial, engineering and biological modeling problems. To overcome the limitations imposed by the use of a single, conforming mesh, we are developing a novel so-called cut finite element framework which allows for a flexible decoupling of the geometry description from the underlying computational grid. For instance, complex geometries only described by some explicit or implicit surface representation can easily be embedded into a structured background mesh. Therefore, this technique may offer many advantages over standard finite element methods that require the generation of a single conforming mesh resolving the full computational domain. A key component in utilizing the full potential of the novel cut finite elements method is to provide efficient and scalable search and cutting algorithms required for the coupling of the unfitted domains. As part of our research project and the allocated computing time, we will investigate strategies to employ data structures and algorithm from the field of computational geometry in a parallel execution model. Additionally, we will also benchmark and test a number of popular finite element frameworks including * FEniCS * deal.ii * mfem for a suitability in HPC computing when non-trivial multi-physics problem have to be solved. Finally, to demonstrate the applicability of cut finite element methods in a high-performance computing context, we intend to solve a series of large-scale, real-life problems with practical relevance for biomedical and industrial applications.