Second order numerical scheme for motion of polygonal curves with constant area speed
This work provides a novel numerical method for simulating area-preserving geometric flows of polygons, which is relevant to computational geometry and materials science.
The authors develop a second-order numerical scheme for polygonal curves moving with constant area speed, proving its accuracy and efficiency through simulations of curvature-driven and advected flows.
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.