Efficient, robust, and highly scalable implicit solver for the simulation of thermoplastic solidification processes

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As a flexible and contact-free joining technology, laser beam welding has increasingly gained importance. Processing of alloys with large melting range poses a challenge due to their solidification cracking tendency. Solidification cracks form due to critical stress and strain states of the dendritic microstructure with interdendritic melt. Despite the high industrial relevance, there are only approaches addressing single aspects of the problem, metallurgically or structurally oriented. The research unit "Solidification Cracking during Laser Beam Welding – High Performance Computing for High Performance Processes" aims at developing quantitative process understanding of the mechanisms of solidification cracking and their relation to process parameters.In collaboration with anotheer project, this subproject is concerned with multi-scale simulations of the processes in the mushy zone in front of the solidification front, where the critical zone for solidification cracks is located. One focus of the present subproject is the improvement and parallel implementation of efficient, robust, and highly scalable implicit solvers for thermoplastic problems. A second focus is the extension of the computational homogenization method FE$^2$ and especially its implementation within the software package FE2TI. Both aspects are essential for successful HPC-simulations located in the mushy zone.In order to solve the upcoming thermoplastic problems, BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) domain decomposition methods will be extended. Both domain decomposition approaches have already proven to be robust and extremely scalable for elasto-plastic problems. Based on our own PETSc-based implementation, which has already shown parallel scalability on some of the world's largest supercomputers and up to several hundred thousand parallel processes, robust coarse spaces for thermoplastic problems with a complex microstructure will be developed. In addition, suitable approximations of these coarse spaces will be investigated to further improve parallel scalability. For an efficient use of modern hardware also adaptive mesh refinement has to be considered, without destroying the parallel load balance.Additionally, an interface to the finite element and material model library FEAP will be added to FE2TI, in order to solve thermoplastic problems on both microscopic and mesoscopic scale. The standards for sustainable software development defined in TP7 will be taken into account, including the Continuous-Benchmarking principle. All further developments of the parallel solvers BDDC and FETI-DP will be incorporated into FE2TI such that the best possible software environment for simulations in the mushy zone is always available.