Computing confined elasticae

TL;DR

This paper introduces a numerical method for computing low-energy elastic curves confined within convex domains, demonstrating convergence, stability, and classifying optimal confined elasticae through simulations.

Contribution

It presents a novel numerical scheme for confined elasticae, proving convergence and stability, and classifies optimal curves within spheres.

Findings

Numerical scheme converges to the continuous model.

Iterative scheme is unconditionally stable.

Simulations classify optimal confined elasticae within spheres.

Abstract

A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an iterative scheme are addressed. Numerical simulations confirm the theoretical results and lead to a classification of observed optimal curves within spheres.