HPC for cut finite element methods
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 moving interfaces can be severely limited by the use of conforming meshes when complex geometries in three spatial dimensions are involved. A related problem is parameter studies with changing geometric domains. 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 example is the design of complex devices, where a seamless rearrangement of subdomains modeling individual device components is highly desirable. Generating a single, conforming mesh for each configuration can severely interrupt the design process. To overcome the limitations imposed by the use of a single, conforming mesh, several novel finite element methods based on cut and composite meshes have been developed in recent years. Such cut finite element methods allow for a flexible decomposition of the computational domain into several, possibly overlapping domains. Moreover, complex geometries only described by some 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. Instead, the challenge becomes to develop stable formulations for the coupling between the various domain parts. This is an highly active research topic, recently attracting greater attention. 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. Furthermore, to demonstrate the applicability of cut and composite mesh 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.