Scalability of the time-to-solution of mortar-based contact problems
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For some time, mortar methods have been the method of choice for modeling surface- coupled problems featuring non-matching grids, given their high accuracy and variational consistency. The substantial increase in numerical complexity resulting from the computation of mortar integrals, particularly in three dimensions, demands an efficient and parallelizable framework. This framework should exhibit good scalability on parallel hardware architectures, such that it is well suited for solving high-fidelity models that may involve several million degrees of freedom. Additional challenges arise when trying to efficiently solve the resulting system of linear equations on parallel computing clusters. It has recently been shown that aggregation based algebraic multigrid (AMG) methods can be used as highly efficient and scalable preconditioners for mortar-based contact problems in saddle-point formulation [2]. Additionally, adopting the dynamic load balancing approach proposed by [1] accelerates parallel evaluations of mortar operators and their linearizations. While it’s been shown that AMG and dynamic load balancing perform well individually in terms of weak [1][2] and strong scaling [1], combined effects are yet to be studied. In this contribution, we assess the effect of the combined application of AMG and dynamicload balancing on the scalability of the time-to-solution of a high fidelity, mortar-based contact simulation with large deformations and present the resulting potential speedup of the HPC framework. REFERENCES [1] M. Mayr and A. Popp. Scalable computational kernels for mortar finite element methods. Engineering with Computers, 2023. [2] T. A. Wiesner, M. Mayr, A. Popp, M. W. Gee, and W. A. Wall. Algebraic multigrid methods for saddle point systems arising from mortar contact formulations. International Journal for Numerical Methods in Engineering, 122(15):3749–3779, 2021.