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

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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.