Fast heat transfer simulation for laser powder bed fusion

Accurate and fast modeling of the temperature distribution and phase transitions in laser powder bed fusion is a major milestone in achieving its quality assurance. Commonly referred to as digital twin technology, the goal is to find agile, fast-to-compute but also sufficiently accurate simulators that can replicate the 3D printing process while enhancing the quality of its outcomes. In this work, we propose a surrogate model for the nonlinear heat transfer equation coupled with subspace projection and randomized sketching, that exploits the accuracy and explainability of finite element time-domain simulation with the computational efficiency of Monte Carlo sampling, applied to the modality of laser powder bed fusion. Focusing on tackling the high-dimensionality imparted from the finite element approximation and the nonlinearity in the governing equations, our surrogate relies on low-dimensional projection with subspace selection and subsequently sub-samples the Picard iterations utilized to solve the projected non-linear system of equations. The projection bases are generated in the process of simulation by combining previous temperature profiles and locally deployed anisotropic Gaussian functions, while the sketching process utilizes efficient sampling without replacement based on approximate optimal sampling distributions. Both the projection and the sketching are designed to implement alongside the printing process, which makes the proposed surrogate capable of handling different process parameters without requiring prior computations offline. A series of numerical experiments are presented to validate the surrogate’s accuracy and reduction in compute time compared to high-fidelity finite element simulations. Although the achieved speed-up can be as a high ten, computational times are still orders of magnitude away from what would be required for real-time computations. The presented methodology allows to handle different printing attributes (laser power and scan speed) and arbitrary thermal conductivity anisotropy.