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

激光焊接作为一种灵活、无接触的连接技术，越来越受到人们的重视。大熔点合金的凝固开裂倾向给其加工带来了挑战。凝固裂纹的形成是由于枝晶组织的临界应力和应变状态以及枝晶间熔体。尽管与工业高度相关，但只有从冶金或结构方面解决问题的单一方面的办法。“激光束焊接过程中的凝固开裂——高性能工艺的高性能计算”研究单位旨在对凝固开裂机理及其与工艺参数的关系进行定量的工艺理解。在与另一个项目的合作下，该子项目涉及凝固前沿前方糊状区过程的多尺度模拟，该区域是凝固裂纹的关键区域。当前子项目的一个重点是改进和并行实现高效，稳健，高度可扩展的热塑性问题隐式求解器。第二个重点是计算均匀化方法FE$^2$的扩展，特别是它在软件包FE2TI中的实现。这两个方面对于位于糊状区的hpc模拟的成功是必不可少的。为了解决即将出现的热塑性问题，BDDC（平衡域分解）和FETI-DP（有限元撕裂和互连-对偶原）域分解方法将得到扩展。对于弹塑性问题，这两种区域分解方法都已被证明具有鲁棒性和高度可扩展性。基于我们自己的基于petsc的实现，它已经在一些世界上最大的超级计算机上显示出并行可扩展性，并且多达数十万个并行过程，将开发具有复杂微观结构的热塑性问题的鲁棒粗空间。此外，将研究这些粗空间的适当近似值，以进一步提高并行可伸缩性。为了有效地利用现代硬件，还必须考虑自适应网格细化，而不破坏并行负载平衡。此外，FE2TI还将加入有限元和材料模型库FEAP的接口，以便在微观和细观尺度上解决热塑性问题。将考虑TP7中定义的可持续软件开发标准，包括持续基准原则。并行求解器BDDC和FETI-DP的所有进一步发展将被纳入FE2TI，以便在糊化区模拟的最佳软件环境始终可用。

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.