Second order numerical scheme for motion of polygonal curves with constant area speed

TL;DR

This paper introduces a second-order numerical scheme for simulating polygonal curves moving with constant area speed, ensuring geometric accuracy and efficiency in modeling boundary motions like curvature-driven flow.

Contribution

It develops a novel second-order scheme for polygonal boundary motion that preserves constant area speed and extends geometric formulas to polygonal analogues.

Findings

The scheme accurately models polygonal boundary motions.

Numerical simulations confirm the scheme's efficiency and precision.

Applicable to various motions like curvature flow and area-preserving flow.

Abstract

We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of general constant area speed motion of polygons. Accuracy and efficiency of our numerical scheme are checked through numerical simulations for several polygonal motions such as motion by curvature and area-preserving advected flow etc.