大规模有限单元分析的鲁棒且并行可扩展的迭代求解方法
Robust and parallel scalable iterative solutions for large-scale finite cell analyses
AI总结：
针对有限单元法在大规模问题中因条件数差而难以使用迭代求解的问题，本文提出一种 Additive-Schwarz 型预处理器，实现了大规模多级 hp 细化有限单元分析的高效并行可扩展迭代求解。
摘要：
有限单元法是一种高度灵活的离散化技术，用于在具有复杂几何形状的域上进行数值分析。通过使用易于划分网格的非边界贴合的 computational domain，可以对广泛的几何模型执行自动化计算。有限单元法以及其他浸入式方法在大型实际和工业问题中的应用，往往由于与这些方法相关的 conditioning 问题而受到限制。这些 conditioning 问题导致研究人员不得不采用直接求解方法，这显著限制了可求解系统的最大规模。与直接求解方法相比，迭代求解器更适合大规模计算，因为它们具有更低的内存需求并且适合并行计算。然而，只有在系统被适当 preconditioned 时，这些优势才能得到利用。在这项工作中，我们提出了一种 Additive-Schwarz 型预处理器，能够实现大规模多级 hp-refined 有限单元分析的高效且并行可扩展的迭代求解。
英文摘要：
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which signifi- cantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.
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