Spectrally accurate algorithm for points redistribution on closed curves

Yunchang Seol*, Ming-Chih Lai

*Corresponding author for this work

研究成果: Article同行評審

摘要

In this paper, we present a novel numerical method that redistributes unevenly given points on an evolving closed curve to satisfy equi-arclength(-like) condition. Without substantial difficulty, it is also capable of remeshing or employing adaptive mesh refinement. The key idea is to find the discrete inverse of the arclength(-like) function in the framework of the Fourier spectral method to obtain overall spectral accuracy. Both equi-arclength and curvature-dependent redistributions are extensively studied, and their spectral accuracy is verified by application to smoothly perturbed points on various curves. We further confirm that our method converges even for the points being perturbed nonsmoothly and randomly. To leverage the robustness of our method, a remeshing technique is applied in which the accuracy is not affected. Application to a periodic planar curve without any modification of our algorithm is also discussed. Then, to show the practical applicability, an evolving curve with large deformation is studied by coupling with point redistribution and remeshing in various flows such as mean curvature flow, Willmore flow, and Stokes flow.

原文English
頁(從 - 到)A3030-A3054
期刊SIAM Journal on Scientific Computing
42
發行號5
DOIs
出版狀態E-pub ahead of print - 1 十月 2020

指紋 深入研究「Spectrally accurate algorithm for points redistribution on closed curves」主題。共同形成了獨特的指紋。

引用此