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

激光焊接作为一种柔性、无接触的连接技术，越来越受到人们的重视。由于具有大熔化范围的合金的凝固开裂倾向，其加工提出了挑战。凝固裂纹的形成是由于枝晶组织与枝晶间熔体的临界应力和应变状态。尽管具有高度的工业相关性，但只有解决问题的单一方面的方法，无论是从结构上还是从功能上。研究单位"激光焊接中的凝固裂纹--高性能工艺的高性能计算"旨在发展对凝固裂纹机理及其与工艺参数关系的定量工艺理解。该子项目与另一个项目合作，关注凝固前沿前糊状区过程的多尺度模拟，凝固裂纹的临界区所在的位置。目前的子项目的一个重点是改进和并行实施的高效，强大的，高度可扩展的隐式求解热塑性问题。第二个重点是计算均匀化方法FE$^2 $的扩展，特别是其在软件包FE2TI中的实现。为了解决即将出现的热塑性问题，BDDC（Balancing Domain Decomposition by Constraints）和FETI-DP（Finite Element Tearing and Interconnecting-Dual Primal）区域分解方法将得到扩展。这两种区域分解方法已经被证明是强大的，非常可扩展的弹塑性问题。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和多达几十万个并行过程，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，适当的近似这些粗糙的空间将被调查，以进一步提高并行可扩展性。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还将增加有限元和材料模型库FEAP的接口，以解决微观和介观尺度上的热塑性问题。将考虑TP 7中定义的可持续软件开发标准，包括连续基准原则。并行求解器BDDC和FETI-DP的所有进一步开发都将被纳入FE2TI，以便始终提供糊状区模拟的最佳软件环境。

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.