Continuous space-time multi-level hp Galerkin-Petrov finite elements for the direct numerical simulation of laser power bed fusion processes

用于激光功率床聚变过程直接数值模拟的连续时空多级 HP Galerkin-Petrov 有限元

• 批准号: 441506233
• 负责人: Professor Dr.-Ing. Stefan Kollmannsberger
• 金额: --
• 依托单位: Lehrstuhl Informatik im Bauwesen
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/441506233?language=en
• 关键词: Continuous; space; time; multi; level

This project aims at developing a new discretizational technology for the analysis of laser powder bed fusion processes (LPBF). LPBF is one of the most important additive manufacturing technologies to produce complex shaped load bearing parts. It is characterized by a multi-scale behavior in space and time. While the process clearly exhibits a multi-physical nature as well, it is especially the prediction of the thermal history which is crucial to this process. However, due to the required spatial resolution as well as the numerous time steps involved, the accurate prediction of the thermal history brings current numerical techniques to their limit.The proposed methodology to be developed in this project is a continuous Galerkin-Petrov finite element formulation in an hp setting which leads to optimal convergence rates. A special focus lies on algorithmic efficiency, for which the discretization will be formulated on hierarchical grids in the spirit of the multi-level hp-method. Further, the proposed formulation will allow for a parallelization in time, which is considered crucial given the time scales involved in the process. Since a boundary-conforming discretization in 4D is not feasible, the developed continuous Galerkin-Petrov finite element formulation on hierarchical grids will be combined with the Finite Cell Method (FCM). The FCM is an embedded domain formulation which allows for a non-boundary conforming discretization on simple grids without loss of accuracy even if the simulated physical artifact possesses a complex shape and topology. The developed methodology will be verified at numerous benchmarks including an analysis of its algorithmic complexity. Additionally, a thorough validation is planned together with the National Institute of Science and Technology, NIST, USA. In a second phase, it is planned to harvest the benefits of time-parallelization on high-performance computers, including a development of suitable parallel solvers. The technology will then be extended for the simulation of other physical phenomena and coupled multi-physical problems.

该项目旨在开发一种用于分析激光粉末床熔化过程（LPBF）的新离散技术。 LPBF 是生产复杂形状承载零件的最重要的增材制造技术之一。它的特点是在空间和时间上的多尺度行为。虽然该过程也明显表现出多物理性质，但热历史的预测对该过程至关重要。然而，由于所需的空间分辨率以及涉及的大量时间步长，热历史的准确预测使当前的数值技术达到了极限。该项目中要开发的方法是连续 Galerkin-Petrov 有限元公式在 hp 设置中，可实现最佳收敛速度。特别关注算法效率，为此，将本着多级 hp 方法的精神在分层网格上制定离散化。此外，所提出的公式将允许时间上的并行化，考虑到过程中涉及的时间尺度，这被认为是至关重要的。由于 4D 中的边界一致离散化是不可行的，因此开发的分层网格上的连续 Galerkin-Petrov 有限元公式将与有限元方法 (FCM) 相结合。 FCM 是一种嵌入式域公式，即使模拟的物理工件具有复杂的形状和拓扑，它也允许在简单网格上进行非边界一致离散化，而不会损失精度。所开发的方法将在众多基准上进行验证，包括对其算法复杂性的分析。此外，还计划与美国国家科学技术研究所 (NIST) 一起进行彻底的验证。在第二阶段，计划在高性能计算机上收获时间并行化的好处，包括开发合适的并行求解器。该技术随后将扩展到其他物理现象和耦合多物理问题的模拟。