In this article, we study the thermal instability that appears from time to time while printing using a 3D printer. To solve the semi-discretized problem at each time-step, we use a scalable parallel algorithm based on a two-level Optimized Restricted Additive Schwarz (ORAS) domain decomposition preconditioner for GMRES. Parallel scalability tests are conducted with comparison against the parallel direct solver MUMPS and the one-level Schwarz method, which show lack of robustness for larger number of processors. 2D numerical tests illustrate that the number of iterations to reach GMRES convergence depends on the state of the physical simulation during time, and that the second level of preconditioning is needed to achieve robustness.

在本文中，我们研究了使用 3D 打印机打印时不时出现的热不稳定性。为了解决每个时间步的半离散问题，我们使用基于两级优化受限加性施瓦茨 (ORAS) 域分解预处理器的 GMRES 可扩展并行算法。并行可扩展性测试与并行直接求解器 MUMPS 和一级 Schwarz 方法进行了比较，这表明对于大量处理器缺乏鲁棒性。二维数值测试表明，达到 GMRES 收敛的迭代次数取决于物理模拟在一段时间内的状态，并且需要第二级预处理来实现鲁棒性。