Research in high performance computing focuses on issues of multi-level preconditioning, the development of space-time finite element methods, and domain decomposition methods.
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 excersize the developed algorithms.
Contacts at IMCS
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
- 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
- Mayr, M., Noll, M.H., Gee, M.W. (2020): A hybrid interface preconditioner for monolithic fluid-structure interaction solvers, Advanced Modeling and Simulation in Engineering Sciences, 7:15, DOI (Open Access)
Current Projects
Space-Time Finite Elements
Space-time finite element methods provide a coherent discretization of space and time for the numerical solution of partial differential equations (PDEs).
Various time-dependent application cases can benefit from the advantages of space-time discretizations, e.g., motions or deformations of the computational domain are directly accounted for by the space-time finite element space. Even a spatial computational domains with time-varying topology can be discretized with a connected boundary-conforming space-time mesh. In addition, the space-time mesh resolution can be adapted to the local accuracy requirements of the problem.
In the field of high performance computing (HPC), advanced meshing capabilities open up a path to parallel-in-time (PinT) computations on complex domains. Since domain-decompositions techniques can be applied to the entire space-time domain, parallelism is no longer limited to the spatial domain. As a candidate for an effective PinT method, the combination of space-time finite elements and multigrid solvers is investigated.
Contacts at IMCS
Key Publications
- von Danwitz M, Voulis I, Hosters N, Behr M (2023): Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems. International Journal for Numerical Methods in Engineering, DOI (Open Access)
- von Danwitz, M., Antony, P., Key, F., Hosters, N., Behr, M. (2021): Four-dimensional elastically deformed simplex space-time meshes for domains with time-variant topology. International Journal for Numerical Methods in Fluids, 93(12): 3490-3506, DOI (Open Access)
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.
Contacts at IMCS
Key Publications
- 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
- Farah, P., Vuong, A.-T., Wall, W.A., Popp, A. (2016): Volumetric coupling approaches for multiphysics simulations on non-matching meshes, International Journal for Numerical Methods in Engineering, 108:1550-1576, DOI
Current Projects
- Algebraic multigrid methods for preconditioning of block systems
- Highly efficient and parallel scalable mortar methods for contact and multi-field problems