We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a function of the arclength through a natural change of variables. The trapezoidal rule is applied to those Fourier-type integrals and the resulting formula fits in the framework of the non-uniform fast Fourier transform. This observation enables to efficiently use an envelope analysis and smoothing filter to generate guidelines for mesh refinement in two singularity formation scenarios. Applications also include a non-iterative construction of the uniform parametrization for an important class of plane curves, which is used in a convergence study of the time-stepping procedure implemented in the previous work by Nitsche and Steen (2004).

我们提出了一种基于信号处理的新型网格细化方案，用于具有轴向对称性的无粘性液滴动力学的边界积分模拟。一个关键思想是通过变量的自然变化直接访问作为弧长函数的主曲率的傅立叶系数。将梯形规则应用于那些傅立叶型积分，并且所得公式适合于非均匀快速傅立叶变换的框架。此观察结果可以有效地使用包络分析和平滑过滤器来生成两种奇异点形成方案中网格细化的准则。应用程序还包括对重要一类平面曲线进行统一参数化的非迭代构造，