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.

中文翻译：

---

使用两级方法的增材制造问题的数值解

近年来，增材制造技术有了显着增长，因为它们能够生产出标准生产技术几乎不可能获得的设计。这种增长反过来又导致对增材工艺数值模拟的需求增加。不幸的是，从计算的角度来看，这种模拟很困难，因为加性问题的特点是存在高度局部非线性，需要在域的一小部分上进行精细的网格分辨率。这些局部高非线性区域随时间在域中移动的事实以及物理域本身随时间演变的事实使这些困难更加复杂。因此，本文通过采用两级技术来解决这些复杂的计算问题。两级方法为解决局部非线性提供了一个自然框架，同时避免了复杂的网格划分操作，例如细化和细化算法。所提出的方法在一系列一维和二维问题上得到验证，以确定所引入的两级方法在增材制造问题上的可行性。