AI 中文总结
针对薄膈肌几何结构的线性弹性问题，采用不拟合最小二乘径向基函数单位分解方法进行求解，推导了其高阶收敛的理论证明，可用于模拟膈肌变形以辅助理解机械通气相关并发症。
AI 中文摘要
人体膈肌对呼吸至关重要，对其进行模拟有助于进一步理解接受机械通气的个体出现的并发症。膈肌几何结构非常薄，因此大多数数值方法对其进行数值模拟存在挑战。本文计算真实膈肌几何结构的变形，该结构被建模为线弹性体，并承受实际边界条件。所使用的方法是不拟合最小二乘径向基函数单位分解方法（unfitted least-squares radial basis function partition of unity method），鉴于其不拟合特性以及所用圆柱 patch 的形状和细化程度，该方法非常适合求解薄几何结构上的问题。我们推导了理论证明，表明该方法对该问题的解具有高阶收敛性。
英文摘要
The human diaphragm is vital for respiration and its simulation can aid in further understanding complications arising in individuals that have been subjected to mechanical ventilation. The diaphragm geometry is very thin and hence its numerical simulation poses a challenge for most numerical methods. In this paper, we compute the deformation of real diaphragm geometries which are modelled as linearly elastic and are subject to realistic boundary conditions. The method used is the unfitted least-squares radial basis function partition of unity method, which is well suited to solve problems on thin geometries given its unfitted nature and the shape and refinement of the cylindrical patches that are used. We derive a theoretical proof showing that the method converges with high order to the solution of this problem.
