Traditionally, the geometric multigrid method is used with nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, the non-nested multigrid method could be exploited in order to handle the burden of hierarchy generation, allowing some flexibility on the choice of the levels. We present a parallel, matrix-free, implementation of the non-nested multigrid method for continuous Lagrange finite elements, where each level may consist of independently partitioned triangulations. Our algorithm has been added to the multigrid framework of the C++ finite-element library deal.II. Several 2D and 3D numerical experiments are presented, ranging from Poisson problems to linear elasticity. We test the robustness and performance of the proposed implementation with different polynomial degrees and geometries.

翻译：传统上，几何多重网格方法通常与嵌套层级结构配合使用。然而，针对极细密非结构化网格构建合适的层级结构通常具有高度复杂性。在此场景下，可利用非嵌套多重网格方法来处理层级生成的负担，从而在层级选择上获得一定灵活性。本文提出了一种面向连续拉格朗日有限元的并行无矩阵非嵌套多重网格实现方案，其中每个层级可由独立分区的三角剖分构成。该算法已集成至C++有限元库deal.II的多重网格框架中。通过从泊松问题到线性弹性的多个二维与三维数值实验，我们测试了不同多项式次数和几何构型下所提实现的鲁棒性与计算性能。