Interpolation-based immersed finite element and isogeometric analysis
Interpolation-based immersed finite element and isogeometric analysis
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DOI：
10.1016/j.cma.2023.115890
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Jennifer E. Fromm;Nils Wunsch;Ru Xiang;H. Zhao;K. Maute;J. A. Evans;D. Kamensky
中科院分区：
文献类型：
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作者：
Jennifer E. Fromm;Nils Wunsch;Ru Xiang;H. Zhao;K. Maute;J. A. Evans;D. Kamensky
我们引入了一种新的浸入式有限元和等几何方法范例，该方法基于将未拟合背景网格中的函数空间插值到前景网格上定义的拉格朗日有限元空间，该前景网格捕获域几何，但在其他方面受到元素质量或连通性的最小约束。这是对等几何分析文献中拉格朗日提取概念的推广，也与有限单元法和材料点法的某些变体以及设计中的自由形式变形概念有关。至关重要的是，插值可以是近似的，而不会牺牲高阶收敛速度，这将本方法与现有的高阶有限单元法、CutFEM和浸入几何方法区分开来。插值范式还允许非侵入性地重用现有的有限元软件进行浸入式分析。我们分析了一个模型问题的基于插值的浸入式范式的特性，并在开源的FEniCS有限元软件上实现了它，将其应用于流体、固体和结构力学中的各种问题，在这些问题上，我们展示了高阶精度和对实际几何形状（如修剪样条补丁）的适用性。
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the domain geometry but is otherwise subject to minimal constraints on element quality or connectivity. This is a generalization of the concept of Lagrange extraction from the isogeometric analysis literature and also related to certain variants of the finite cell and material point methods, as well as the concept of free-form deformation from design. Crucially, the interpolation may be approximate without sacrificing high-order convergence rates, which distinguishes the present method from existing high-order finite cell, CutFEM, and immersogeometric approaches. The interpolation paradigm also permits non-invasive reuse of existing finite element software for immersed analysis. We analyze the properties of the interpolation-based immersed paradigm for a model problem and implement it on top of the open-source FEniCS finite element software, to apply it to a variety of problems in fluid, solid, and structural mechanics where we demonstrate high-order accuracy and applicability to practical geometries like trimmed spline patches.