Spectrally Accurate Simulation of Axisymmetric Vesicle Dynamics

TL;DR

This paper introduces a meshless, spectrally accurate numerical method for simulating axisymmetric vesicle dynamics with adaptive reparameterization and error control, improving efficiency and precision in soft matter physics simulations.

Contribution

The authors develop a novel meshless spectral method with adaptive reparameterization and gauge dynamics for accurate, efficient vesicle simulations in viscous media.

Findings

Achieves high accuracy in vesicle shape and dynamics simulations.

Reduces computational cost by adaptive harmonic reduction.

Maintains stability and accuracy near the symmetry axis.

Abstract

We present a meshless numerical method for simulating the dynamics of axisymmetric vesicles in a viscous medium. Key innovations include: (1) adaptive reparameterization based on local length scales, reducing the number of required harmonics; (2) gauge dynamics for maintaining optimal parameterization; (3) error control near the symmetry axis; and (4) spectrally accurate quadrature schemes for singular integrals. The method achieves high accuracy and computational efficiency for simulating lipid bilayer dynamics and related problems in soft matter physics.