Numerical solution of additive manufacturing problems using a two‐level method

Additive manufacturing techniques have grown significantly in recent years due to their ability to produce designs almost impossible to obtain with standard production technologies. This growth has in turn led to increased demand for numerical simulation of additive processes. Unfortunately, such simulations are difficult from the computational point of view, since additive problems are characterized by the presence of highly local nonlinearities requiring fine mesh resolutions on small portions of the domain. These difficulties are compounded by the fact that such regions of local high nonlinearities move in the domain with time, and further, by the fact that the physical domain itself evolves with time. Accordingly, the present article addresses these complex computational issues by employing a two‐level technique. The two‐level method provides a natural framework for the resolution of localized nonlinearities while avoiding the need for complex meshing operations, such as refinement‐and‐derefinement algorithms. The proposed approach is validated on a series of one‐ and two‐dimensional problems to establish the viability of the introduced two‐level method for additive manufacturing problems.