We perform a followup computational study of the recently proposed space–time first order system least squares ( FOSLS ) method subject to constraints referred to as CFOSLS where we now combine it with the new capability we have developed, namely, parallel adaptive mesh refinement (AMR) in 4D. The AMR is needed to alleviate the high memory demand in the combined space time domain and also allows general (4D) meshes that better follow the physics in space–time. With an extensive set of computational experiments, performed in parallel, we demonstrate the feasibility of the combined space–time AMR approach in both two space plus time and three space plus time dimensions.

我们对最近提出的时空一阶系统最小二乘法（FOSLS）方法进行后续计算研究，该方法受到称为CFOSLS的约束，现在我们将其与我们开发的新功能（即并行自适应网格细化（AMR））结合起来）以4D模式显示。需要AMR来减轻组合时空域中的高存储需求，并且还允许通用（4D）网格更好地遵循时空物理学。通过大量并行执行的计算实验，我们证明了在两个空间加时间和三个空间加时间维度上使用时空组合AMR方法的可行性。