We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized implementations. We only operate on the bounding faces of finite elements without considering their lower-dimensional topological features and demonstrate the potential of the presented methods using a newly written open-source library. First, we analyze a Fichera corner and show that the framework does not increase runtime and memory consumption when compared against the classical p-version of the finite element method. Then, we compute a transient example with dynamic refinement and derefinement, where we also obtain the expected convergence rates and excellent performance in computing time and memory usage.

中文翻译：

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任意维度的高效多级 hp 有限元

我们提出了一种高效的算法框架，用于构建多级 hp-bases，该框架使用面向数据的方法，可以轻松扩展到任意数量的维度，并为性能优化的实现提供自然框架。我们只对有限元的边界面进行操作，而不考虑它们的低维拓扑特征，并使用新编写的开源库展示了所提出方法的潜力。首先，我们分析了一个 Fichera 角，并表明与有限元方法的经典 p 版本相比，该框架不会增加运行时间和内存消耗。然后，我们计算一个具有动态细化和去细化的瞬态示例，我们还获得了预期的收敛速度以及计算时间和内存使用方面的优异性能。