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

用于模拟热塑性凝固过程的高效、稳健且高度可扩展的隐式求解器

• 批准号: 457126257
• 负责人: Professor Dr. Axel Klawonn
• 金额: --
• 依托单位: Lehrstuhl für Numerische Mathematik und Wissenschaftliches Rechnen
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/457126257?language=en
• 关键词: Efficient; robust; highly; scalable; implicit

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.

激光焊接作为一种柔性、无接触的连接技术，日益受到重视。由于合金的凝固开裂倾向，大熔点合金的加工是一个挑战。凝固裂纹是由于枝晶组织与枝晶间熔体的临界应力和应变状态所致。尽管具有很高的工业相关性，但只有从冶金或结构上解决问题的单一方面的办法。“激光焊接过程中的凝固裂纹--高性能工艺的高性能计算”这一研究单元旨在发展对凝固裂纹机理及其与工艺参数之间关系的过程的定量理解。该子项目与另一个项目合作，对凝固裂纹临界区所在的凝固前沿前方的糊状区的过程进行多尺度模拟。本子项目的一个重点是改进和并行实现热塑性问题的高效、健壮和高度可扩展的隐式求解器。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。为了解决即将到来的热塑性问题，我们将扩展BDDC和FETI-DP两种区域分解方法。这两种区域分解方法对于弹塑性问题都已被证明是健壮的和极具伸缩性的。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和多达数十万个并行过程上显示出并行可伸缩性，将开发用于具有复杂微观结构的热塑性问题的健壮的粗空间。此外，还将研究这些粗略空间的适当近似，以进一步提高并行可伸缩性。为了有效地使用现代硬件，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还将增加与有限元和材料模型库FEAP的接口，以解决微观和介观尺度的热塑性问题。将考虑到项目方案7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的所有进一步开发都将被合并到FE2TI中，以便始终可以使用最好的软件环境来进行糊状区的模拟。