论文标题
强大而可扩展的H-自适应聚合无限元素，用于接口问题
Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems
论文作者
论文摘要
这项工作介绍了一种新颖的，完全健壮的，高度可观的，$ h $的适应性汇总的未有限元方法，用于大规模接口椭圆形问题。新方法是基于在高度可观的笛卡尔森林网状发动机上的汇总有限元方法的最新分布式内存实现。它遵循经典的方法，即在接口处弱耦合非匹配离散以建模界面的内部不连续性。我们建议将单域并行细胞聚集方案的自然扩展到有限数量的界面问题。它直接导致具有笛卡尔产品结构的有限元元素空间。我们通过对几个复杂的泊松和线性弹性基准进行的标准数值分析和详尽的数值实验证明，新技术享有以下属性：适当的属性，相对于剪切的位置和最佳对比度，最佳（$ h $ aptaptive）（$ h $ - $ -H $ - 适用性）的近似性能，较高的估计性和易于实现。结果，该方法为大规模界面问题提供了有用的有限元求解器，以部分微分方程建模。
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the aggregated finite element method atop a highly-scalable Cartesian forest-of-trees mesh engine. It follows the classical approach of weakly coupling nonmatching discretisations at the interface to model internal discontinuities at the interface. We propose a natural extension of a single-domain parallel cell aggregation scheme to problems with a finite number of interfaces; it straightforwardly leads to aggregated finite element spaces that have the structure of a Cartesian product. We demonstrate, through standard numerical analysis and exhaustive numerical experimentation on several complex Poisson and linear elasticity benchmarks, that the new technique enjoys the following properties: well-posedness, robustness with respect to cut location and material contrast, optimal ($h$-adaptive) approximation properties, high scalability and easy implementation in large-scale finite element codes. As a result, the method offers great potential as a useful finite element solver for large-scale interface problems modelled by partial differential equations.
