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
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
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.