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.

本计画旨在发展一种新的离散化技术，以分析雷射粉末床熔合过程。LPBF是生产复杂形状承载部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，但对该过程至关重要的是热历史的预测。然而，由于所需的空间分辨率以及涉及的众多的时间步长，准确预测的热历史带来了目前的数值技术，以其limit.The建议的方法，在这个项目中开发的是一个连续的Galerkin-Petrov有限元公式在HP设置，从而导致最佳的收敛速度。一个特别的重点在于算法的效率，其中的离散化将制定分层网格的精神，多层次的惠普方法。此外，拟议的提法将允许在时间上并行化，鉴于这一进程所涉的时间尺度，这一点被认为至关重要。由于在4D中的边界协调离散化是不可行的，开发的连续Galerkin-Petrov有限元公式的分层网格将结合有限单元法（FCM）。FCM是一种嵌入式域公式，它允许在简单网格上进行非边界一致离散化，即使模拟的物理工件具有复杂的形状和拓扑结构，也不会损失精度。所开发的方法将在众多的基准测试，包括其算法复杂性的分析进行验证。此外，还计划与美国国家科学技术研究所（NIST）一起进行全面验证。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。然后，该技术将扩展到其他物理现象和耦合多物理问题的模拟。