关于虚拟域方法中连续与不连续拉格朗日乘子的选择
On the Choice of Continuous and Discontinuous Lagrange Multipliers in Fictitious-Domain Methods
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中文总结 AI 辅助
本文比较了虚拟域方法中连续与不连续拉格朗日乘子两种离散格式，发现连续格式局部误差更小，不连续格式失配衰减更规律且原始误差更小。
中文摘要 AI 辅助
本文考察了使用分布式拉格朗日乘子的虚拟域方法（FD-DLM），该方法通过独立网格处理椭圆界面问题，无需界面与背景网格匹配。研究比较了使用连续和不连续乘子空间时两种稳定的低阶FD-DLM离散格式。研究区分了逐单元满足弱耦合约束与两个离散原始场之间差异的大小。数值实验表明，连续格式通常产生更小的局部误差和最大失配值，而不连续格式在网格细化时失配的减小更为规律，且原始误差更小。
英文摘要
This article examines the Fictitious-Domain approach using Distributed Lagrange Multipliers (FD-DLM), a method that handles elliptic interface problems with separate meshes without requiring the interface to match the background mesh. It compares two stable, low-order FD-DLM discretizations when using both continuous and discontinuous multiplier spaces. The study distinguishes between satisfying the weak coupling constraint per element and the size of the discrepancy between the two discrete primal fields. Numerical experiments indicate that the continuous formulation usually yields smaller local errors and maximum mismatch values, while the discontinuous formulation shows a more regular decrease in mismatch as the mesh is refined and has smaller primal errors.
发表机构
- General Studies Department, Jubail Industrial College（公共基础系，朱拜勒工业学院）
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