Our research in the area of high performance computing focuses on issues of multi-level preconditioning, the development of domain decomposition methods and parallel computing.
Contacts at IMCS
Multi-Level Preconditioning
When solving large FEM models of complex problems, robust and problem-specific iterative methods and preconditioners are key for the efficient solution of the arising linear systems of equations. Since out-of-the-box preconditioning techniques do not deliver optimal performance for complex systems, IMCS develops problem-specific preconditioning techniques by incorporating the underlying physics into the design of the preconditioner.
To obtain scalable algorithms even for large-scale parallel simulations, research codes at IMCS employ and develop algebraic multigrid (AMG) methods within the Trilinos/MueLu framework. In particular, we design level transfer operators and smoothers tailored to the particularities of the underlying physical problem and provide open-source implementations of our algorithms via Trilinos/MueLu.
The Data Science & Computing Lab operates an HPC cluster to exersize the developed algorithms.
Key Publications
- Firmbach, M., Steinbrecher, I., Popp, A., Mayr, M. (2024): An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction, Computer Methods in Applied Mechanics and Engineering, 431:117256, DOI (Open Access)
- Mayr, M., Berger-Vergiat, L., Ohm, P., Tuminaro, R. S. (2022): Non-invasive multigrid for semi-structured grids, SIAM Journal on Scientific Computing, 44(4): A2734-A2764, DOI
- Wiesner, T.A., Mayr, M., Popp, A., Gee, M.W., Wall, W.A. (2021): Algebraic multigrid methods for saddle point systems arising from mortar contact formulations, International Journal for Numerical Methods in Engineering, 122:3749-3779, DOI (Open Access) , arXiv
Current Projects
Domain Decomposition
Domain decomposition (DD) methods are an essential building block of efficient parallel and high-performance computing in computational engineering based on partial differential equations. At IMCS, we not only use state-of-the-art DD approaches for parallel partitioning and for preconditioning of iterative solvers, but carry out cutting-edge research on mortar methods for non-overlapping mesh and domain coupling. Within the parallel research code 4C, our group has established one of the leading software frameworks worldwide for mortar methods with its features ranging from classical FEM mesh tying or IGA patch coupling over dual Lagrange multiplier spaces and dynamic load balancing techniques to numerous single-field and multi-field problems, including contact mechanics, thermo-mechanics and fluid-structure interaction. Our expertise on mortar methods has not only contributed to new scientific insights in applications such as battery modeling or turbine blade-to-disc joints, but also fuels commercial FEM code development at ANSYS, Inc. through a long-standing partnership.
Key Publications
- Mayr, M., Popp, A. (2023): Scalable computational kernels for mortar finite element methods, Engineering with Computers, 39(5):3691-3720, DOI (Open Access)
- Hesch, C., Khristenko, U., Krause, R., Popp, A., Seitz, A., Wall, W.A., Wohlmuth, B.: Frontiers in mortar methods for isogeometric analysis, Preprint, submitted for publication, arXiv
- Wunderlich, L., Seitz, A., Alaydin, M.D., Wohlmuth, B., Popp, A. (2019): Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity, Computer Methods in Applied Mechanics and Engineering, 346:197-215, DOI
Current Projects
- Efficient numerical algorithms for solving systems of linear equations
- Highly efficient and parallel scalable mortar methods for contact and multi-field problems
Parallel Computing
Today's demand for simulation models with high accuracy and fidelity usually bring along the necessity to run very large computational models. To combine such models with available hardware resources, IMCS tackles specific topics in parallel computing in order to deploy such computations on today's supercomputers as well as use their hardware resources efficiently. Particular research questions arise in mixed-dimensional and/or multi-physics systems, where the workload of the individual computational domains might differ vastly and, thus, require customized scheduling and load balancing techniques to use all available computing hardware to the same extent. Traditionally focusing distributed memory architectures and the message passing interface (MPI) for inter-node communication, on-node parallelization and accelerators such as graphical processing units (GPUs) play an increasing role in research and applications.Key Publications
- Firmbach, M., Steinbrecher, I., Popp, A., Mayr, M. (2024): An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction, Computer Methods in Applied Mechanics and Engineering, 431:117256, DOI (Open Access)
- Mayr, M., Popp, A. (2023): Scalable computational kernels for mortar finite element methods, Engineering with Computers, 39(5):3691-3720, DOI (Open Access)